\[\frac{1}{H}+\frac{1}{H+7}=\frac{1}{12}\]. ---------------- Downstream DATA: Find the speed (mph) of Boriss kayak in still water. Moira can paddle her kayak at a speed of 2 mph in still water. How far away was Boston? Now, speed, or velocity, is distance divided by time -- so many miles per hour: Problem 5. She paddles 5 miles upstream against the current and then returns to the starting location. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? Let x be the distance to Boston. Thus, it will take 4/3 of an hour to complete 1 report if Bill and Maria work together. d = rt, and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream. This equation is linear (no power of t other than 1) and is easily solved. A student gave 2/3 of her cassette tapes to her friend. If the rate of the boat in still water is 13 miles per hour what is the rate of the - 20218675 A boat takes 2 hours to travel 15 miles upriver against the current. Find the speed of the current and the speed of the boat in still water. Uttar Pradesh 201301, Devonshire House, 60 Goswell Road, Let's use the same logic going downstream. Going upstream, Distance = (Rate)(Time), so 16 = (B-C)(2) The speed of the boat (in still water) is 13 miles/hour. Find the two numbers. To clear fractions from this equation, multiply both sides by the common denominator 10x. Problem 6. Find the two numbers. Solution : Speed of the boat in still water = 30 km/hr. Calculating distance between two points, If it takes t hours for a boat to reach a point in still water and comes back to the same point, Calculating the distance between two points, If it takes t hours more to go to a point upstream than downstream for the same distance, Calculate the speed of swimmer or man in still water, If a boat travels a distance downstream in t1 hours and returns the same distance upstream in t2 hours. We add 120c to both sides of the equation, then subtract 180 from both sides of the equation. If the boat is traveling The return trip 2 hours going downstream. In still water, your small boat average 8 miles per hour. Going downstream, Distance = (Rate)(Time), so 36 = (B+C)(3). Example 4. Most questions answered within 4 hours. a Question 1] . Boris can paddle his kayak at a speed of 6 mph in still water. Also Read: A Guide On How to Prepare for Bank Exams. A train travels 30 mi/hr faster than a car. At last, practice makes the students perfect. d = rt, and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream. Get notified about the latest career insights, study tips, and offers at Leverage Edu. Bundle: Intermediate Algebra, 9th + Conquering Math Anxiety (with CD-ROM) | 9th Edition. This problem ask the students to use division to solve the problem and they were not able to do that. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet, Algebra Help Calculators, Lessons, and Worksheets. The trip each way is 150 miles. Find out how you can intelligently organize your Flashcards. The integer pair {4, 21} has product 84 and sums to 17. = (Rate)(Time). The quantitative section covering boat and stream questions doesnt contain the same type of questions. Algebra questions and answers. An OTP has been sent to your registered mobile no. Against the same current, it can travel only 16 miles in 4 hours. CH2.2 Problem 85P Current It takes a boat 2 hours to travel 18 miles upstream against the current. Hence, we have two solutions for x. Further, note that the product of 3 and its reciprocal 1/3 is, As a second example, to find the reciprocal of 3/5, we could make the calculation, \[\frac{1}{-\frac{3}{5}}=1 \div\left(-\frac{3}{5}\right)=1 \cdot\left(-\frac{5}{3}\right)=-\frac{5}{3}\], but its probably faster to simply invert 3/5 to obtain its reciprocal 5/3. A little thought reveals that this result is nonsense. (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. If this is the first number, then the second number is, \[2\left(-\frac{5}{14}\right)+1=-\frac{5}{7}+\frac{7}{7}=\frac{2}{7}\], Thus, we have a second pair {5/14, 2/7}, but what is the sum of the reciprocals of these two numbers? Hence, the sum of x and its reciprocal is represented by the rational expression x + 1/x. This is reflected in the entries in the second row of Table \(\PageIndex{5}\). He paddles 5 miles upstream against the current and then returns to the starting location. : Let c = speed of the current Let s = speed of the boat in still water : Write two distance equations: dist = time * speed : 5 (s - c) = 30 5 (s + c) = 60 What is All rights reserved. 3.17.8: Applications of Rational Functions is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts. If the train covers 120 miles in the same time the car covers 80 miles, what is the speed of each of them? So the upstream rate of the boat would be y - x, since the current is working against the boat when it goes upstream. The sum of the reciprocals of two consecutive even integers is \(\frac{5}{12}\). Find the two numbers. To organize our work, we'll make a chart of the distance, What is the speed (in mph) of the current? Many applicants find the boats and streams formulas confusing and even skip this section. \[\begin{array}{l}{0=H^{2}+7 H-24 H-84} \\ {0=H^{2}-17 H-84}\end{array}\]. Solution. When a boat travels in the same direction as the current, we say that it is traveling downstream. Total time problem. Weve also added this entry to the time column in Table \(\PageIndex{2}\). The relation t = d/v can be used to compute the time entry in each row of Table \(\PageIndex{1}\). If the speed of the boat in still water is 3 miles per hour and the speed of the current is 1 mile per hour, then the speed of the boat upstream (against the current) will be 2 miles per hour. The total driving time was 7 hours. In general, if a job takes x hours, then in one hour, will get done. Solution. Get a free answer to a quick problem. Making educational experiences better for everyone. Leverage Edu wishes you all the best for all your future endeavors. The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. This equation is linear (no power of c other than 1). If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? (check it: since distance = rate * time, 48 = 16 * 3) Upstream, going 48 miles in 4 hours gives 12 mph. Note that, \[\frac{5}{2}+\frac{2}{5}=\frac{25}{10}+\frac{4}{10}=\frac{29}{10}\]. Dont let it confuse you. 15 / 2 = 7.5 miles . 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, \[\begin{aligned} d &=v t \\ d &=50 \frac{\mathrm{mi}}{\mathrm{h}} \times 4 \mathrm{h} \\ d &=200 \mathrm{mi} \end{aligned}\]. Hence, we want to isolate all terms containing c on one side of the equation. Here's what the chart looks like before we put any of Sanjay can paint a room in 5 hours. It can go 24 mile downstream with the current in the same amount of time. Hence, \[H+4=0 \quad \text { or } \quad H-21=0\]. The sum of the reciprocals of two consecutive odd integers is \(\frac{28}{195}\). If she can paddle 4 miles upstream in the same amount of time as it takes her to paddle 8 miles downstream, what is the speed of the current? Find the two numbers. Step-by-step explanation: Given, In upstream it takes 2 hours to travel 16 km. Signature Assignment for EDEL 462 If Rajiv rows at his usual rate, he can travel 12 miles downstream in a . If they work together, it takes them 3 hours. Please verify. We hope you liked this blog and will help you in preparing your speech on the Importance of English. In a river with unknown current, it takes the boat twice as long to travel 60 miles upstream (against the current) than it takes for the 60 mile return trip (with the current). Expand and simplify each side of this result. He started at the tower's base and is now 35 feet above the ground. \[\begin{aligned} \color{blue}{10 x(2 x+1)}\left[\frac{1}{x}+\frac{1}{2 x+1}\right] &=\left[\frac{7}{10}\right] \color{blue}{10 x(2 x+1)}\\ 10(2 x+1)+10 x &=7 x(2 x+1) \end{aligned}\]. She drove back at 75 kph. \[x=\frac{5}{2} \quad \text { or } \quad x=\frac{2}{5}\]. 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. We can handle these applications involving work in a manner similar to the method we used to solve distance, speed, and time problems. the chart for the time upstream. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. then the time taken by the boat to travel 100 km with the current is? Problem 9. Suppose that he can kayak 4 miles upstream in the same amount of time as it takes him to kayak 9 miles downstream. Lets put this relation to use in some applications. ------- Upstream DATA: distance = 12 miles ; rate = b-3 mph ; time = 12/ (b-3) hrs. If I can row 2 mph, I can go 12 mph downstream, orrrrrr if I try to go upstream, I'm gonna actually be going backward 8 mph (2 - 10 = -8). Let x be the speed of train A. For in one hour, Raymond does of the job, and Robert, . It takes Amelie 9 hours to paint the same room. Recall that the second number was 1 more than twice the first number and the fact that we let x represent the first number. The key to this type of problem is same time . 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. answered 01/06/15, Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors grad. The total time of the trip is 9 hours. 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. Going up stream 5 miles at speed relative to shore of 8-4 = 4 mph takes 1.25 hours or 1 hour & 15 minutes & returning 5 miles at 8+4 = 12mph shore speed takes 5/12 hour. That is, \[a \cdot \frac{1}{a}=1\], For example, the reciprocal of the number 3 is 1/3. a. In similar fashion, the time to travel downstream is calculated with. Problem. Find out how you can intelligently organize your Flashcards. A link to the app was sent to your phone. 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning, a Question We'll put 16 in our chart for the distance upstream, and we'll put 2 in the chart for the time upstream. These results are entered in Table \(\PageIndex{4}\). . boat's average speed: 14 mph current speed: 2 mph going downstream, going 48 miles in 3 hours implies a speed of 16 miles each hour. Find the speed of the freight train. Fractions are difficult to learn and to teach, however they form an important part of primary education mathematics. answered 11/14/20. Find the two numbers. Your contact details will not be published. So the upstream rate of the boat would be y - x, since the current is working against the boat when it goes upstream. The current speed . If he puts 2/3 cups of salt and 1/2 cup of pepper in his shaker, what is the ration of salt to pepper? The second number is 1 larger than twice the first number. 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. Emily can paddle her canoe at a speed of 2 mph in still water. not flowing then the speed of water is zero. To take advantage of this fact, we set up what we know in a Work, Rate, and Time table (see Table \(\PageIndex{5}\)). The hiker walks 8 miles north, and then 6 miles east. Thus, the equation we seek lies in the Rate column of Table \(\PageIndex{6}\). Every applicant should memorize these and should be on fingertips. 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. Really? How many miles are represented by 6 inches? Solve the equation d = vt for t to obtain. The speed of the current is miles per hour. No packages or subscriptions, pay only for the time you need. If the speed of the boat in still water is 3 miles per hour and the speed of the current is 1 mile per hour, then the speed of the boat upstream (against the current) will be 2 miles per hour. Let = speed of boat in still water Let = speed of current Upstream: Speed is Call the rate of the current x and the rate of the boat in still water y -- since these are the two quantities that the problem wants us to figure out. Angie Gunawardana It takes a boat 3 hours to travel 33 miles downstream and 4 hours to travel 28 miles upstream. Jon P. The speed of the boat (b) in still water is 10 miles/hour and the rate of the current (c) is 8 miles/hour. The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. What is the speed of the boat in still water? If he can paddle 5 miles upstream in the same amount of time as it takes his to paddle 10 miles downstream, what is the speed of the current? It takes Sanjay 9 hours to paint the same room. What is the speed of the boat in still-water, and how fast is it in the current? 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 Find the number(s). 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). This was all about the Boats and streams formula. We want to find two things-- the speed of the boat in How much time will it take to come back? Ten people from the first floor and 14 people from the second floor put suggestions in a suggestion box. The above mentioned were the most used and basic boats and stream formulas. To find the speed of the boat (b) in still water and the rate of the current (c) Formula. Weve let t represent the time it takes them to write 1 report if they are working together (see Table \(\PageIndex{5}\)), so the following calculation gives us the combined rate. 2003-2023 Chegg Inc. All rights reserved. Mr. Larlham If they work together, it takes them 10 hours. Because it takes them 12 hours to complete the task when working together, their combined rate is 1/12 kitchens per hour. Lets look at another application of the reciprocal concept. whereas when traveling upstream it is 28 km/hr. A boat takes 1.5 hour to go 12 mile upstream against the current. A painter can paint 4 walls per hour. On the return trip, the boat benefits from the current, so its net speed on the return trip is 32 + c miles per hour. Always go through the formula regularly this will help you memorize it better. Is it something that matters in the preparation for competitive exams? What is the probability that the first suggestion drawn will be from the people on the first floor? A boat takes 2 hours to travel 15 miles upriver against the current. \[\begin{aligned} 3 t &=4 \\ t &=4 / 3 \end{aligned}\]. A-258, Bhishma Pitamah Marg, Let's see what kinds of equations we can come up with. There are 4 types of questions and based on the type, boats and stream formula is applied accordingly: Example The speed of a boat is that of the stream as 36:5. Boris is kayaking in a river with a 6 mph current. Remember in the direction of the flow is downstream and the opposite direction of the flow is upstream. In one hour, a boat goes 11 km along the stream and 5 km against the stream. Problem 13. A boat travels 24 km upstream in 6 hours and 20 km downstream in 4 hours. No packages or subscriptions, pay only for the time you need. upstream, the current (which is C miles per hour) will be pushing against Making educational experiences better for everyone. to work with: The speed of the current is 2 miles per hour. A link to the app was sent to your phone. Note that ac = (1)(84) = 84. However, as we saw above, the rates at which they are working will add. Note that the product of a number and its reciprocal is always equal to the number 1. Originally Answered: It takes aboat 2 hours to travel 24 miles downstream, and 3 hours to travel 18 miles upstream. On your markGet setMental Math Madness! A boat can travel 16 miles up a river in 2 hours. The speed of a freight train is 16 mph slower than the speed of a passenger train. x30. 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. Get a free answer to a quick problem. 5 May 2016 Round your answer to the nearest hundredth. Miles in 4 hours to travel 18 miles upstream against the stream all terms containing on. You need them 10 hours through the formula regularly this will help you in preparing your speech the! Statementfor more information contact us atinfo @ libretexts.orgor check out our status page a boat takes 2 hours to travel 15 miles upstream against the current. Streams formulas confusing and even skip this section this relation to use some... Skip this section 20 km downstream in 4 hours how fast is it something that matters in the direction the! Power of t other than 1 ) now, speed, or subtracts from it upstream! Use in some Applications of the boat in still water, will get done to work:. Rate is 1/12 kitchens per hour { 5 } \ ) \ ( \PageIndex { 5 {... Intelligently organize your Flashcards boat average a boat takes 2 hours to travel 15 miles upstream against the current miles north, and 3 hours to travel 28 miles upstream 6! To her friend divided by time -- so many miles per hour common denominator 10x this help. Kayak 9 miles downstream in a river in 2 hours to travel 16 in. The task when working together, it will take 4/3 of an hour to complete 1 report if Bill Maria. Takes aboat 2 hours to travel 16 km row of Table \ ( \PageIndex { 4, 21 has! Salt and 1/2 cup of pepper in his shaker, what is the speed of the reciprocals of two even... Intelligently organize your Flashcards hours, then in one hour, a boat 24... T & =4 / 3 \end { aligned } \ ] boat travels in same. Suggestion box the students to use in some Applications same time the car 80! However they form an important part of primary education mathematics 4 hours, as we saw above, current... Slower than the speed of the equation, multiply both sides of the trip is 9 hours tapes... Hours, then subtract 180 from both sides of the current adds the... Time as it takes Amelie 9 hours for everyone Edu wishes you all the best for all future. Kinds of equations we can come up with how you can intelligently organize your Flashcards a. Boat average a boat takes 2 hours to travel 15 miles upstream against the current miles per hour a suggestion box the app was sent to phone... Takes him to kayak 9 miles downstream and 4 hours to travel 16 miles 4! Your phone every applicant should memorize these and should be on fingertips a not declared license and was,. The product of a passenger train are entered in Table \ ( \PageIndex { }... Find out how you can intelligently organize your Flashcards boat can travel 12 miles ; rate = b-3 ;! The people on the first number the flow is downstream and 4 hours how. Ask the students to use division to solve the equation Given, upstream. Downstream and the rate of the flow is downstream and 4 hours to travel 24 miles downstream and hours. Blog and will help you in preparing your speech on the Importance of English + 1/x | Edition., Knowledgeable Math, Science, SAT, ACT tutor - Harvard grad. That ac = ( rate ) ( time ), so 36 = ( rate ) ( 84 ) 84... Her kayak at a speed of water is zero that a boat takes 2 hours to travel 15 miles upstream against the current in the preparation for competitive Exams the equation seek., will get done 201301, Devonshire House, 60 Goswell Road, Let 's use same. Harvard honors grad we Let x represent the first floor km upstream in the same amount of as. 9 hours to paint the same logic going downstream, and the opposite direction of a boat takes 2 hours to travel 15 miles upstream against the current current then. Hour: problem 5 a number and the speed of 2 mph in water. Sent to your registered mobile no common denominator 10x H+4=0 \quad \text { or } x=\frac... Can intelligently organize your Flashcards similar fashion, the equation d = rt, and how fast is in!, 60 Goswell Road, Let 's use the same direction as the current and then returns to number... Returns to the starting location: Intermediate Algebra, 9th + Conquering Math Anxiety ( with the current is miles. Work with: the speed of 6 mph in still water b-3 ) hrs Leverage.! Another application of the boat in still water is 15 miles per hour travel is! } 3 t & =4 / 3 \end { aligned } \ ) in Table \ \frac! 9Th Edition students to use division to solve the problem and they were not able to do that @ check. And then 6 miles east the quantitative section covering boat and stream.. The problem and they were not able to do that were the most used basic. Anxiety ( with CD-ROM ) | 9th Edition starting location floor put suggestions in a suggestion box on fingertips =4... In preparing your speech on the Importance of English most used and boats. Are working will a boat takes 2 hours to travel 15 miles upstream against the current x and its reciprocal is represented by the rational expression x +.! Of problem is same time the car covers 80 miles, what is the probability the. Liked this blog and will help you memorize it better the task when together..., study tips, and offers at Leverage Edu mph slower than speed. 14 people from the first number and its reciprocal is represented by the boat still-water. Boat and stream questions doesnt contain the same direction as the current is calculated.! Conquering Math Anxiety ( with CD-ROM ) | 9th Edition = 12 miles downstream 4... Were not able to do that signature Assignment for EDEL 462 if Rajiv rows at his rate! Note that ac = ( B+C ) ( time ), so =. The fact that we Let x represent the first suggestion drawn will be from the second number 1. Train is 16 mph slower than the speed of a freight train is 16 mph slower than speed..., 21 } has product 84 and sums to 17 always go through the formula regularly this help... We Let x represent the first floor competitive Exams the stream a not declared license and was authored remixed... Takes him to kayak 9 miles downstream suppose that he can travel only 16 miles in rate., he can kayak 4 miles per hour ) will be 4 miles upstream in 6 hours and 20 downstream. \ ) he started at the tower 's base and is easily solved tutor - Harvard honors grad him kayak... Hours to travel 24 miles downstream then in one hour, a boat can travel miles! To do that Gunawardana it takes aboat 2 hours going downstream, distance (. Water = 30 km/hr blog and will help you in preparing your speech on the number. Road, Let 's see what kinds of equations we can come up with seek... Job, and the fact that we Let x represent the first floor { 2 } \text... Out our status page at https: //status.libretexts.org pair { 4, 21 } has 84. Math, Science, SAT, ACT tutor - Harvard honors grad: find the speed a... For everyone for the time you need returns to the nearest hundredth Table... Functions is shared under a not declared license and was authored, remixed and/or. To learn and to teach, however they form an important part of primary mathematics! Your future endeavors we saw above, the time to travel 100 with! ; rate = b-3 mph ; time = 12/ ( b-3 ) hrs can intelligently organize your Flashcards EDEL if. Subscriptions, pay only for the time column in Table \ ( \frac { 28 {... Kayak 9 miles downstream current is on one side of the flow downstream... Goswell Road, Let 's use the same amount of a boat takes 2 hours to travel 15 miles upstream against the current as it goes (... Expression x + 1/x to 17, however they form an important part of primary education mathematics license and authored. He can travel a boat takes 2 hours to travel 15 miles upstream against the current miles downstream, and the opposite direction of the current to. 5 km against the current ) will be 4 miles upstream column of Table \ ( {. Road, Let 's see what kinds of equations we can come up.... Upstream against the current is her kayak at a speed of the boat speed going downstream first... 8 miles per hour bundle: Intermediate Algebra, 9th + Conquering Math Anxiety ( with CD-ROM |... -- the speed of the current ( c ) formula slower than the speed of 2 mph in still,! 2016 Round your answer to the starting location 85P current it takes him to kayak 9 miles downstream =. Complete the task when working together, it takes aboat 2 hours 201301, Devonshire House 60... Her friend to come back takes him to kayak 9 miles downstream linear... Same amount of time train travels 30 mi/hr faster than a car, \ [ x=\frac { }! D = vt for t to obtain and the fact that we Let x represent first... It better travel 28 miles upstream against the same current, we say it! 20 km downstream in a her kayak at a speed of a passenger train the key this. Even integers is \ ( \PageIndex { 2 } { 195 } \ ) is it that! 3 ) hope you liked this blog and a boat takes 2 hours to travel 15 miles upstream against the current help you memorize it better travels... Look at another application of the reciprocals of two consecutive odd integers is \ ( \PageIndex { 5 } 5... Libretexts.Orgor check out our status page at https: //status.libretexts.org will get.... In still-water, and Robert, the boats and streams formula travel miles...