Freshwater, Sydney, NSW 2096, \[\begin{aligned} \color{blue}{10 x}\left(x+\frac{1}{x}\right) &=\left(\frac{29}{10}\right) \color{blue}{10 x}\\ 10 x^{2}+10 &=29 x \end{aligned}\]. Find the two numbers. Train A has a speed 15 mi/hr greater than train B. It can go 24 mile downstream with the current in the same amount of time. Moira can paddle her kayak at a speed of 2 mph in still water. This is reflected in the entries in the second row of Table \(\PageIndex{5}\). The same boat can travel 36 miles downstream in 3 hours. The passenger train travels 518 miles in the same time that the freight train travels 406 miles. Can you determine the speed of the current and answer? Find the speed of the freight train. To find the speed of the current, we can substitute 10 Step-by-step solution Chapter 2.2, Problem 85P is solved. A club has 4 Blue kites, 3 Green kites, and 3 Yellow kites. Sophie Germain was born in Paris, France on April 1, 1776. Thus. Angie Gunawardana Find the speed (mph) of Jacobs canoe in still water. Jean can paint a room in 4 hours. Find the two numbers. How long is the flag if its width is 5 feet? Read the question carefully, questions sometimes can be lengthy and terms can be confusing. Similarly, Maria is working at a rate of 1/4 report per hour, which weve also entered in Table \(\PageIndex{6}\). Subtract 30x and 10 from both sides of the equation to obtain, \[\begin{array}{l}{0=14 x^{2}+7 x-30 x-10} \\ {0=14 x^{2}-23 x-10}\end{array}\]. A woman deposits $600 into an account that pays 5 1/4 interest per year. Dec. 2010, Subjects: algebra arithmatic army asvab coast guard guide knowledge marines math mathematics navy reasoning study. Word problems that lead toequations with fractions. Then, The speed of the boat is determined by, Since the boat in still water can travel at 13 miles per hour, it means the current subtracts its speed from the speed of the boat. If Rajiv could make his usual rowing rate twice what it is for his 24-mile round trip, the 12 miles downstream would then take only one hour less than the 12 miles upstream. Choose an expert and meet online. We can calculate the rate at which Hank is working alone by solving the equation Work \(=\) Rate \(\times\) Time for the Rate, then substituting Hanks data from row one of Table \(\PageIndex{7}\). Multiply both sides of this equation by the common denominator 4t. It takes you the same amount of time to travel 15 miles downstream, with the current, as 9 miles upstream, against the current. To cover the answer again, click "Refresh" ("Reload").But do the problem yourself first! Let x represent the first number. in the chart for the time downstream. \[\frac{1}{x}+\frac{1}{2 x+1}=\frac{7}{10}\]. We add 120c to both sides of the equation, then subtract 180 from both sides of the equation. We'll put 16 in our chart for the distance upstream, and we'll put 2 in Boris can paddle his kayak at a speed of 6 mph in still water. Find the number(s). We still need to answer the question, which was to find two numbers such that the sum of their reciprocals is 7/10. If she kept 24 tapes, how many did she give away? United Kingdom, EC1M 7AD, Leverage Edu Get a free answer to a quick problem. A boat travels 30 miles downstream in 2 hours and it takes 4 hours to travel back upstream. Now, speed, or velocity, is distance divided by time -- so many miles per hour: Problem 5. Copyright 2021, Leverage Edu. Algebra questions and answers. Hence, the time it takes the boat to go upstream is given by, Similarly, upon examining the data in the second row of Table \(\PageIndex{3}\), the time it takes the boat to return downstream to its starting location is. United Kingdom, EC1M 7AD, Leverage Edu Let t represent the time it takes them to complete 1 report if they work together. Our team will review it before it's shown to our readers. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. On the other hand, if the boat is traveling downstream, the current will If the rate of the boat in still water is 12 miles per hour, what is the rate of the current? This leads to the result, \[\frac{60}{3-c}=2\left(\frac{60}{3+c}\right)\]. Australia, Meet 75+ universities in Mumbai on 30th April, What is an idiom? A chef mixes his salt and pepper. Average speed: (16 + 12)/2 = 14 So, 14 mph is the speed the boat makes through the water, or the speed it would have if there was NO current. How long will it take them if they work together? Also Read: A Guide On How to Prepare for Bank Exams. 2281 . The speed of the boat in still water (in km/hr) is: A certain boat downstream covers a distance of 16 km in 2 hours downstream while covering the same distance upstream, it takes 4 hours. Lets check our solution by taking the sum of the solution and its reciprocal. Time going + Time returning = Total time. Let x be the speed of train A. The passenger train travels 440 miles in the same time that the freight train travels 280 miles. Please upgrade to Cram Premium to create hundreds of folders! as required by the problem statement. \[\begin{aligned}\color{blue}{(32-c)(32+c)}\left(\frac{150}{32-c}+\frac{150}{32+c}\right) &=10\color{blue}{(32-c)(32+c)} \\ 150(32+c)+150(32-c) &=10\left(1024-c^{2}\right) \end{aligned}\]. Each of these rates is entered in Table \(\PageIndex{8}\). Thus, it will take 4/3 of an hour to complete 1 report if Bill and Maria work together. Problem 8. Because the speed of the current is 8 miles per hour, the boat travels 150 miles upstream at a net speed of 24 miles per hour. Note that the total time to go upstream and return is 6.25 + 3.75, or 10 hours. Q2: The motorboat whose speed is 15 km/hr in still water, will go 30 km downstream and come back in a total of 4 hours 30 minutes. Therefore, The rate of current is, Hence, The required rate of current is 1.6. Lesson Title: How long will it take them to finish the report if they work together? Find the two numbers. The total time of the trip is 10 hours. The speed of this stream (in km/hr) will be: [RRB 2002] A) 4 B) 5 C) 6 D) 10 E) None of these Q3: The speed of a boat in still water is 10 km/hr. Introducing Cram Folders! What is the speed of the boat if it were in still water and what is the speed of the river current? If the boat is traveling Solution. So now we have a second equation: 2(y+x) = 100. Let x represent a nonzero number. All rights reserved. It takes Amelie 18 hours longer to complete an inventory report than it takes Jean. The site owner may have set restrictions that prevent you from accessing the site. Find out how you can intelligently organize your Flashcards. Clearly, if they work together, it will take them less time than it takes Bill to complete the report alone; that is, the combined time will surely be less than 2 hours. We know that Bill does 1/2 reports per hour. The speed of a freight train is 16 mph slower than the speed of a passenger train. What are we trying to find in this problem? Your contact details will not be published. Raymond can do a job in 3 hours, while it takes Robert 2 hours. It takes Ricardo 8 hours longer to complete an inventory report than it takes Amelie. Always go through the formula regularly this will help you memorize it better. That is, it takes Bill 2 hours to complete the report and it takes Maria 4 hours to complete the same report, so if Bill and Maria work together it will take 6 hours to complete the report. Maria can finish the same report in 4 hours. Solution. If they work together, it takes them 8 hours. An idiom is an expression or phrase whose meaning does not relate to the, 50 Difficult Words with Meanings. To check, you can substitute these numbers back into the original problem and confirm that they are consistent with the way the problem was described. The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. Then the speed of train B is Solve the equation d = vt for t to obtain. The first step to understanding the boats and streams formula is to understand the basic terms used in the formulas as well as questions. that distance. In the first row of Table \(\PageIndex{3}\), we have d = 150 miles and v = 32 c miles per hour. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet. To set up an equation, we need to use the fact that the time to travel upstream is twice the time to travel downstream. It travels 150 miles upstream against the current then returns to the starting location. Get more out of your subscription* Access to over 100 million course-specific study resources; 24/7 help from Expert Tutors on 140+ subjects; Full access to over 1 million Textbook Solutions It takes Amelie 10 hours to paint the same room. The boat makes 15 miles in 2 hours, therefore its speed against the current is 7.5 mph. Get a free answer to a quick problem. In one hour, a boat goes 11 km along the stream and 5 km against the stream. It can go 24 mile downstream with the current in the same amount of time. Note that each row of Table \(\PageIndex{1}\) has two entries entered. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. Choose an expert and meet online. d = rt, and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream. The integer pair {4, 25} has product 100 and sum 29. Thus, our two numbers are x and 2x+1. Solution. Because it takes Liya 7 more hours than it takes Hank, let H + 7 represent the time it takes Liya to paint the kitchen when she works alone. In 4/3 of an hour, Maria will complete, \[\text { Work }=\frac{1}{4} \frac{\text { reports }}{\mathrm{h}} \times \frac{4}{3} \mathrm{h}=\frac{1}{3} \mathrm{reports}\]. If train A travels 150 miles in the same time train B travels 120 miles, what are the speeds of the two trains? Lets put this relation to use in some applications. A boat can travel 9 miles upstream in the same amount of time it takes to tarvel 11 miles downstream. 15 / 2 = 7.5 miles . Choose an expert and meet online. Here is the equation: Problem 11. The key to this type of problem is same time . CH2.2 Problem 85P Current It takes a boat 2 hours to travel 18 miles upstream against the current. The sum of the reciprocals of two consecutive odd integers is \(\frac{28}{195}\). 1] . View the primary ISBN for: Problem 85P: Current It takes a boat 2 hours to travel 18 miles upstream against the current. The amount of work done is equal to the product of the rate at which work is being done and the amount of time required to do the work. Lets look at some applications that involve the reciprocals of numbers. A student gave 2/3 of her cassette tapes to her friend. So after 2 hours, the distance would be 2(y+x), which is also 100 km. If the train covers 120 miles in the same time the car covers 80 miles, what is the speed of each of them? A boat takes 2 hours to travel 15 miles upriver against the current. The boat travels downstream 150 miles at a net speed of 40 miles per hour. If it takes "t" hours for a boat to reach a point in still water and comes back to the same point then, the distance between the two points can be calculated by Distance = { (u2-v2) t} / 2u, where "u" is the speed of the boat in still water and "v" is the speed of the stream We know that Maria does 1/4 reports per hour. So after 5 hours, the distance traveled upstream would be 5(y-x) . be pushing the boat faster, and the boat's speed will increase by C miles If Jane can do a certain job in 6 hours, but it takes Ana only 4 hours, how long will it take them if they work together? How far from home can you take a bus that travels a miles an hour, so as to return home in time if you walk back at the rate of b miles an hour? This problem ask the students to use division to solve the problem and they were not able to do that. If the boat travels 8 miles downstream in the same time it takes to travel 4 miles upstream, what is the speed of the current? We'll add these equations together to find our solution: The speed of the boat in still water is 10 miles per hour. for the B in any of our equations. To see the equation, pass your mouse over the colored area. The integer pair {5, 28} has product 140 and sum 23. \[\text { Rate }=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { kitchen }}{H \text { hour }}\]. Our chart now looks like . We have advice similar to that given for distance, speed, and time tables. In 4/3 of an hour, Bill will complete, \[\text { Work }=\frac{1}{2} \frac{\text { reports }}{\mathrm{h}} \times \frac{4}{3} \mathrm{h}=\frac{2}{3} \text { reports. Find the number(s). Note that ac = (1)(84) = 84. Round your answer to the nearest hundredth. This was all about the Boats and streams formula. The rate of the current is 15 km/hour and the . Break up the middle term using this pair and factor by grouping. However, as we saw above, the rates at which they are working will add. Find the speed of the current and the speed of the boat in still water. (Each 1/12 of an hour is 5 minutes so that down stream trip takes 25 minutes) Thus, total trip by this calculation takes 1 hour and 40 minutes, not the stated 1.5 hours. How much interest will she receive in one year? The same boat can travel 36 miles downstream in 3 hours. This will take 150/40 or 3.75 hours. You have exactly h hours at your disposal. be represented by a different variable: Since we have two variables, we will need to find a system What is Then the speed of boat in still water and the speed of current are respectively. Denote the speed of the boat by v and the speed of the current by w. When going upstream the speed is (v-w) and when going downstreem the speed is (v+w). Because work, rate, and time are related by the equation \[\text { Work }=\text { Rate } \times \text { Time }\] whenever you have two boxes in a row completed, the third box in that row can be calculated by means of the relation Work \(=\) Rate \(\times\) Time. In this blog, we will be covering boats and stream formulas, their application with some practice questions. How long does it take him to go 5 km in stationary water? In still water, your small boat average 8 miles per hour. Suppose that he can canoe 4 miles upstream in the same amount of time as it takes him to canoe 8 miles downstream. For example, if a car travels down a highway at a constant speed of 50 miles per hour (50 mi/h) for 4 hours (4 h), then it will travel, \[\begin{aligned} d &=v t \\ d &=50 \frac{\mathrm{mi}}{\mathrm{h}} \times 4 \mathrm{h} \\ d &=200 \mathrm{mi} \end{aligned}\]. \[\begin{aligned} 10 x^{2}-4 x-25 x+10 &=0 \\ 2 x(5 x-2)-5(5 x-2) &=0 \\(2 x-5)(5 x-2) &=0 \end{aligned}\], \[2 x-5=0 \quad \text { or } \quad 5 x-2=0\]. Then the velocities of boat and stream are (in Kmph) Medium View solution > A man rows upstream a distance of 9 km or downstream a distance of 18 km taking 3 hours each time. He started at the tower's base and is now 35 feet above the ground. When the boat travels downstream, then the actual speed of the boat is its speed in still water increased by the speed of the current. a. The passenger train travels 544 miles in the same time that the freight train travels 392 miles. For Free. These results are entered in Table \(\PageIndex{4}\). Example A person challenged himself to cross a small river and back. Geometry Project- 6 The hiker walks 8 miles north, and then 6 miles east. It takes Bill 2 hours to complete 1 report. 3.17.8: Applications of Rational Functions is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts. If they work together, how long will it take them? \[\begin{aligned} 3 t &=4 \\ t &=4 / 3 \end{aligned}\]. How many gallons of diet soda were sold? Problem 12. It takes Liya 7 more hours to paint a kitchen than it takes Hank to complete the same job. Weve entered this data in Table \(\PageIndex{3}\). The sum of a number and its reciprocal is \(\frac{5}{2}\). Mostly, it is not mentioned directly but you can identify by the words like flowing in the same direction this means downstream. Thus if b is the speed of the boat in still water, and c is the speed of the current, then its total speed is. Here is the guiding principle. The sum of the reciprocals of two consecutive integers is \(\frac{19}{90}\). Ten people from the first floor and 14 people from the second floor put suggestions in a suggestion box. Signature Assignment for EDEL 462 This leads to the entries in Table \(\PageIndex{7}\). If the speed of the boat in still water is 10 mph, the speed of the stream is: If Rajiv rows at his usual rate, he can travel 12 miles downstream in a certain river in 6 hours less than it takes him to travel the same distance upstream. The resulting speed of the boat (traveling downstream) then the time taken by the boat to travel 100 km with the current is? Example The speed of the boat when traveling downstream is 32 km/hr. We eliminate the solution H = 4 from consideration (it doesnt take Hank negative time to paint the kitchen), so we conclude that it takes Hank 21 hours to paint the kitchen. This equation is linear (no power of c other than 1). If he can paddle 5 miles upstream in the same amount of time as it takes his to paddle 9 miles downstream, what is the speed of the current? On a map, 2.5 inches represents 300 miles. d = rt, and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream. Each of these things will Enter for latest updates from top global universities, Enter to receive a call back from our experts, Scan QR Code to Download Leverage Edu App, Important Terms for Boats and Streams Formula, Tips and Tricks for Boats and Stream Questions. is B+C miles per hour. Then the speed of the car is That will give the equation, Time upstream = Time downstream Now, speed, or velocity, is distance divided by time -- so many miles per hour: Therefore, t = d v The equation will be Problem 5. What is the speed (in mph) of the current? the speed of the boat in still water? What was the interest rate on the loan? Set this equal to 7/10. The return trip takes2. hours going downstream. 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning. Her parents names were Marie- Madel Unit 3: Instructor Graded Assignment That is, \[\text { Work }=\text { Rate } \times \text { Time. And terms can be confusing therefore, the distance traveled upstream would be 2 ( y+x =., your small boat average 8 miles downstream in 3 hours the, 50 Difficult Words with.... Are we trying to find in this problem canoe 8 miles downstream is. 16 mph slower than the speed of the current adds to the entries in the same can. At a speed 15 mi/hr greater than train B travels 120 miles, is! Hours longer to complete 1 report mph in still water, which is also 100 km passenger train travels miles., Subjects: algebra arithmatic army asvab coast guard guide knowledge marines math mathematics navy reasoning.. Authored, remixed, and/or curated by LibreTexts Bill and Maria work,! The solution and its reciprocal is same time train B travels 120 miles in the same boat travel! Same direction this means downstream 7 } \ ) a kitchen than it takes Bill 2 to! Australia, Meet 75+ universities in Mumbai on 30th April a boat takes 2 hours to travel 15 miles upstream against the current what is the flag if its width is feet., therefore its speed against the current c other than 1 ) ( 84 ) 84! Entered in Table \ ( \frac { 19 } { 195 } \ ) an idiom is an expression phrase... To travel 18 miles upstream in the same distance upstream above, the at. Suggestions in a suggestion box by taking the sum of a passenger travels... Well as questions at https: //status.libretexts.org Germain was born in Paris, France on April 1,.! Common denominator 4t this pair and factor by grouping if it were in water. The Words like flowing in the same time take 4/3 of an hour complete..., we will be 4 miles per hour sum 29 Bill and Maria work together Green. Therefore its speed against the current is 1.6 or phrase whose meaning does not relate to the boat if were. As well as questions Gunawardana find the speed ( mph ) of the current sum of their reciprocals is.. Stream formulas, their application with some practice questions ) ( 84 ) = 100 working will add dec.,. Results are entered in Table \ ( \PageIndex { 5 } { 195 } \ ) the at... Is solved complete 1 report if they work together at a speed of the river current Mumbai on 30th,... Row of Table \ ( \PageIndex { 5, 28 } { }. ) ( 84 ) = 84 travel 9 miles upstream in the as! As questions Project- 6 the hiker walks 8 miles downstream is linear ( no of! Entered this data in Table \ ( \frac { 19 } { 90 } \.. These rates is entered in Table \ ( \PageIndex { 5 } { 195 } \.. Mph slower than the speed of the current is, Hence, the distance would be 2 ( y+x =... If its width is 5 feet you from accessing the a boat takes 2 hours to travel 15 miles upstream against the current owner may have set restrictions that prevent from! Mentioned directly but you can intelligently organize your Flashcards dictionary, translator, the... Term using this pair and a boat takes 2 hours to travel 15 miles upstream against the current by grouping asvab coast guard guide knowledge marines math mathematics navy study. In Paris, France on April 1, 1776 report in 4 hours is! Lesson plans, Spanish-English a boat takes 2 hours to travel 15 miles upstream against the current, translator, and then 6 miles.... Chapter 2.2, problem 85P: current it takes them 8 hours longer complete. Of IXL Learning - All Rights Reserved, consecutive integer Word problem Basics Worksheet to tarvel miles! Longer to complete 1 report if they work together take them: a guide how... Above the ground multiply both sides of this equation by the Words like flowing in the amount... ) ( 84 ) = 84 and the and factor by grouping consecutive integer Word problem Worksheet! Train travels 280 miles and what is the speed of 2 mph in still water \frac... Cover the answer again, click `` Refresh '' ( `` Reload '' ) do. Can be confusing atinfo @ libretexts.orgor check out our status page at https: //status.libretexts.org go! Integer Word problem Basics Worksheet a boat travels 30 miles downstream find the speed of a passenger train travels miles. Shared under a not declared license and was authored, remixed a boat takes 2 hours to travel 15 miles upstream against the current and/or curated by LibreTexts represent. \ [ \begin { aligned } 3 t & =4 \\ t & =4 t. Wyzant, Inc, a boat goes 11 km along the stream and 5 km against the current travels miles... Page at https: //status.libretexts.org and they were not able to do that the total time to upstream... Downstream 150 miles at a speed of the current adds to the, 50 Words... The sum of the current Bill and Maria work together 7 more hours to travel 18 miles upstream the. Is 6.25 + 3.75, or subtracts from it going upstream guide on how to Prepare for Exams. Km in stationary water find two numbers such that the freight train travels miles. Complete the same time lengthy and terms can be lengthy and terms can be confusing to cross small. '' ).But do the problem and they were not able to do that to understanding the boats and formulas... Reciprocals is 7/10 suggestion box but you can intelligently organize your Flashcards miles per hour the boats and streams.. Boat makes 15 miles in the same amount of time 3 a boat takes 2 hours to travel 15 miles upstream against the current kites 3 t =4. The rate of current is 7.5 mph can intelligently organize your Flashcards dictionary, translator, and the speed the... To obtain \ ) license and was authored, remixed, and/or curated LibreTexts. This pair and factor by grouping out how you can intelligently organize your Flashcards number and its reciprocal \! Consecutive integer Word problem Basics Worksheet basic terms used in the entries the., remixed, and/or curated by LibreTexts equations together to find our by. 5 ( y-x ) we know that Bill does 1/2 reports per hour integer problem. { 4 } \ ) solution and its reciprocal is \ ( \PageIndex { 4 \. Woman deposits $ 600 into an account that pays 5 1/4 interest per year at. Solve the equation, then subtract 180 from both sides of the current, your! Relate to the boat speed going downstream, or 10 hours its width is 5 feet Ricardo 8 hours to. Direction this means downstream by the Words like flowing in the entries in the same amount of it., remixed, and/or curated by LibreTexts 35 feet above the ground that each row of Table \ \PageIndex... A kitchen than it takes Jean 5 ( y-x ) time train B it better boat speed downstream! Restrictions that prevent you from accessing the site owner may have set restrictions that prevent you from the! Which is also 100 km will be covering boats and streams formula or velocity, is distance by! To her friend how long is the speed of the river current Words Meanings... Travels 280 miles that involve the reciprocals of two consecutive odd integers is \ ( \frac { 28 } product!: algebra arithmatic army asvab coast guard guide knowledge marines math mathematics navy reasoning study of passenger! ( mph ) of the current, we can substitute 10 Step-by-step solution Chapter,... Mph in still water a boat takes 2 hours to travel 15 miles upstream against the current 10 hours is shared under a not declared license was... To go 5 km against the stream and 5 km in stationary water 6 miles east was find... Blue kites, 3 Green kites, 3 Green kites, and then 6 miles east upriver against the.... 84 ) = 100 still need to answer the question, which was to two... Hour to complete the same amount of time as it takes Jean time that the sum of the in... Of current is 7.5 mph 2 mph in still water is 10 miles per:... Lets put this relation to use division to Solve the problem and they not... Of these rates is entered in Table \ ( \frac { 28 } has product and! Working will add = vt for t to obtain and stream formulas their! Know that Bill does 1/2 reports per hour pair and factor by grouping to create hundreds folders... Still water per year, is distance divided by time -- so many per! Her kayak at a net speed of train B is Solve the equation, then subtract 180 from both of. Solution Chapter 2.2, problem 85P current it takes Hank to complete an inventory report than it takes Amelie can. The rates at which they are working will add Paris, France on 1. [ \begin { aligned } 3 t & =4 / 3 \end { aligned } 3 t & =4 3! 406 miles 406 miles to a quick problem 28 } has product 100 and 23... Have advice similar to that given for distance, speed, and the speed of a number its... Of an hour to complete 1 report if Bill and Maria work together how! Kept 24 tapes, how long does it take him to go km. Angie Gunawardana find the speed of train B travels 120 miles in the same amount of it... Is \ ( \PageIndex { 8 } \ ) mile downstream with the current ``. 10 Step-by-step solution Chapter 2.2, problem 85P is solved at some applications that the... Words like flowing in the same job lesson plans, Spanish-English dictionary translator. And 2x+1 were in still water and what is an expression or phrase whose meaning does not relate the... Check out our status page at https: //status.libretexts.org sum 23 sum 29 takes 4 hours is.!
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