. 2003-2023 Chegg Inc. All rights reserved. In this direction, the current works WITH the boat's engine, so the rate would be y + x. Mark M. A man has painted 1/5 of a tower. Find the speed of the current and the speed of the boat in still water. Thus, our two numbers are x and 2x+1. Thus, it will take 4/3 of an hour to complete 1 report if Bill and Maria work together. \[\begin{aligned} \color{blue}{10 x}\left(x+\frac{1}{x}\right) &=\left(\frac{29}{10}\right) \color{blue}{10 x}\\ 10 x^{2}+10 &=29 x \end{aligned}\]. answered 11/14/20. The sum of a number and its reciprocal is \(\frac{41}{20}\). Uttar Pradesh 201301, Devonshire House, 60 Goswell Road, The boat goes along with the stream in 5 hours and 10 minutes. No packages or subscriptions, pay only for the time you need. Let x represent a nonzero number. For Free. How long will it take them to finish the report if they work together? Jacob is canoeing in a river with a 2 mph current. 5600 = ___________________ What is the rate of the boat in still water and what is the rate of the current? It will take 30 hours to travel 60 miles at this rate. He started at the tower's base and is now 35 feet above the ground. A little thought reveals that this result is nonsense. which is 100 km. The speed of the current is miles per hour. Clearly, working together, Bill and Maria will complete 2/3 + 1/3 reports, that is, one full report. A boat takes 2 hours to travel 15 miles upriver against the current. She drove back at 75 kph. Interest and Loan Concepts A train travels 30 mi/hr faster than a car. Algebra questions and answers. Mostly, it is not mentioned directly but you can identify by the words like flowing in the same direction this means downstream. Lets try to use the ac-test to factor. It takes Sanjay 7 hours to paint the same room. Now, speed, or velocity, is distance divided by time -- so many miles per hour: Problem 5. Find the two numbers. The sum of the reciprocals of two consecutive even integers is \(\frac{11}{60}\). that distance. 3.17.8: Applications of Rational Functions is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts. She paddles 5 miles upstream against the current and then returns to the starting location. We'll put this information in our chart: Each row in the chart will give us an equation. We know that Maria does 1/4 reports per hour. Example A person challenged himself to cross a small river and back. __________________ 3. CH2.2 Problem 85P Current It takes a boat 2 hours to travel 18 miles upstream against the current. Similarly, Maria is working at a rate of 1/4 report per hour, which weve also entered in Table \(\PageIndex{6}\). Most questions answered within 4 hours. United Kingdom, EC1M 7AD, Leverage Edu When we developed the Equations of Motion in the chapter on quadratic functions, we showed that if an object moves with constant speed, then the distance traveled is given by the formula. Step-by-step explanation: Given, In upstream it takes 2 hours to travel 16 km. Then. Lets look at another application of the reciprocal concept. Katrina drove her car to Boston at a speed of 100 kph (kilometers per hour). \[x=\frac{5}{2} \quad \text { or } \quad x=\frac{2}{5}\]. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved. Find the two numbers. Their reciprocals, respectively, are 1/x and 1/(2x + 1). A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. Find the speed of the current. The total time of the trip is 10 hours. Find the two numbers. The speed of the boat in still water is Medium View solution > Many applicants find the boats and streams formulas confusing and even skip this section. we need to write our two equations. Upstream- When the boat is flowing in the opposite direction of the stream, it is called Upstream. . We want to find two things-- the speed of the boat in Going upstream, Distance = (Rate)(Time), so 16 = (B-C)(2) You will only be able to solve these questions if you have memorized the boats and streams formula. Moira can paddle her kayak at a speed of 2 mph in still water. This equation is linear (no power of c other than 1). Note that the time to travel upstream (30 hours) is twice the time to travel downstream (15 hours), so our solution is correct. How long is the flag if its width is 5 feet? 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. If the faucet is running but the drain is open, how long will it take to fill the bathtub? Solution. So, let x answer the question. be represented by a different variable: Since we have two variables, we will need to find a system The speed of the current is 5 miles per hour. a. Get a free answer to a quick problem. Here are some practice questions that will help you understand the pattern of questions and for self-evaluation. Let's say I'm in a 10 mph current in a canoe. Since we are told that in still water (no current), the boat would be making 12 mph, it follows therefore that the current's speed must be the difference of 12 - 7.5, or 4.5 mph. 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? \[\begin{aligned}\color{blue}{(4 t)}\left[\frac{1}{2}+\frac{1}{4}\right] &=\left[\frac{1}{t}\right]\color{blue}{(4 t)} \\ 2 t+t &=4 \end{aligned}\]. If the rate of the boat in still water is 12 miles per hour, what is the rate of the current? Legal. Please select the correct language below. Therefore, the time of travel is, Note how weve filled in this entry in Table \(\PageIndex{2}\). The hiker walks 8 miles north, and then 6 miles east. This will take 150/40 or 3.75 hours. 1. The speed of the boat (b) in still water is 10 miles/hour and the rate of the current (c) is 8 miles/hour. Hence, we want to isolate all terms containing c on one side of the equation. Let's use the same logic going downstream. Example A boat, while going downstream in a river covered a distance of 50 miles at an average speed of 60 miles per hour. Delhi 110024, A-68, Sector 64, Noida, Solution. Going downstream, it can travel 60 miles in the same amount of time. Bundle: Intermediate Algebra, 9th + Conquering Math Anxiety (with CD-ROM) | 9th Edition. If the second number is 1 larger than twice the first number, then the second number can be represented by the expression 2x + 1. (check it: since distance = rate * time, 48 = 16 * 3) Upstream, going 48 miles in 4 hours gives 12 mph. How long it takes the faster one. Angie Gunawardana 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. We weren't able to detect the audio language on your flashcards. A boat travels 24 km upstream in 6 hours and 20 km downstream in 4 hours. The key to this type of problem is same time. Please sign in to share these flashcards. How long does it take Hank to complete the job if he works alone? In one hour, a boat goes 11 km along the stream and 5 km against the stream. Then the speed of the car is On the other hand, if x = 2/5, then its reciprocal is 5/2. Making educational experiences better for everyone. 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? Freshwater, Sydney, NSW 2096, Required fields are marked *. not flowing then the speed of water is zero. On a map, 2.5 inches represents 300 miles. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. Then the speed of train B is We start by recalling the definition of the reciprocal of a number. We can handle these applications involving work in a manner similar to the method we used to solve distance, speed, and time problems. The boat travels at miles per hour in still water. We'll add these equations together to find our solution: The speed of the boat in still water is 10 miles per hour. so we have 2 equations which must be solved . to work with: The speed of the current is 2 miles per hour. Jean can paint a room in 4 hours. Same time problem: Upstream-Downstream. That will give the equation. He calculated the speed of the river that day as 1 km/hr. Find the speed (mph) of Jacobs canoe in still water. Current It takes a boat 2 hours to travel 18 miles upstream against the current. Or, What is the hardest exam in the world? Unit 3 focuses on interest and loan concepts covered in your reading of Chapter 11: Si Fractions The reciprocal of x is 1/x. Find the two numbers. \[\begin{aligned} \color{blue}{10 x(2 x+1)}\left[\frac{1}{x}+\frac{1}{2 x+1}\right] &=\left[\frac{7}{10}\right] \color{blue}{10 x(2 x+1)}\\ 10(2 x+1)+10 x &=7 x(2 x+1) \end{aligned}\]. Lesson Title: Freshwater, Sydney, NSW 2096, It takes Hank 21 hours to complete the kitchen, so he is finishing 1/21 of the kitchen per hour. Krishan W. Her parents names were Marie- Madel Unit 3: Instructor Graded Assignment If the train covers 120 miles in the same time the car covers 80 miles, what is the speed of each of them? How far away was Boston? A boat takes 2 hours to travel 15 miles upriver against the current. The speed of a freight train is 19 mph slower than the speed of a passenger train. 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? document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); 150 Common: Difficult Idioms with Examples. A student gave 2/3 of her cassette tapes to her friend. That is, the second number is 5. Because it takes them 12 hours to complete the task when working together, their combined rate is 1/12 kitchens per hour. Without knowing the accurate boats and streams formula it is impossible for any applicant to solve the question. Note that we simply invert the number 3 to obtain its reciprocal 1/3. be pushing the boat faster, and the boat's speed will increase by C miles A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes . Is it something that matters in the preparation for competitive exams? The total driving time was 7 hours. Set this equal to 7/10. answered 02/17/15, Olubunmi B. In 4/3 of an hour, Maria will complete, \[\text { Work }=\frac{1}{4} \frac{\text { reports }}{\mathrm{h}} \times \frac{4}{3} \mathrm{h}=\frac{1}{3} \mathrm{reports}\]. Lets put this relation to use in some applications. 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? For in one hour, Raymond does of the job, and Robert, . Let x be how long will it take them if they work together. The trip each way is 150 miles. Subtract 30x and 10 from both sides of the equation to obtain, \[\begin{array}{l}{0=14 x^{2}+7 x-30 x-10} \\ {0=14 x^{2}-23 x-10}\end{array}\]. Expand and simplify each side of this result. . 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. Together, they can complete the same job in 12 hours. \[\begin{array}{l}{0=14 x^{2}+5 x-28 x-10} \\ {0=x(14 x+5)-2(14 x+5)} \\ {0=(x-2)(14 x+5)}\end{array}\], \[x-2=0 \quad \text { or } \quad 14 x+5=0\], These linear equations are easily solved for x, providing, \[x=2 \quad \text { or } \quad x=-\frac{5}{14}\]. . Most questions answered within 4 hours. Boats and streams formula-based questions might feel a bit tricky and confusing but after a few practice sessions, you will be able to solve like a pro. Emily can paddle her canoe at a speed of 2 mph in still water. 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. The passenger train travels 518 miles in the same time that the freight train travels 406 miles. If the rate of the boat in still water is 13 miles per hour what is the rate of the - 20218675 The sum of the reciprocals of two consecutive integers is \(\frac{19}{90}\). Each of these rates is entered in Table \(\PageIndex{8}\). It takes the same time for the boat to travel 5 miles upstream as it does to travel 10 miles downstream. As a result of the EUs General Data Protection Regulation (GDPR). Remain calm and read the whole question carefully and try to understand the boats and streams formula that can be applied to solve the question. It is important to check that the solution satisfies the constraints of the problem statement. 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. How many gallons of diet soda were sold? Note that the total time to go upstream and return is 6.25 + 3.75, or 10 hours. It will take 30 hours to travel 60 miles at this rate. in the chart for the time downstream. Answer: 1 hour 15 minutes. Train A has a speed 15 mi/hr greater than train B. In boats and streams questions, upstream and downstream are not mentioned. 19 . What is the speed of the current in miles per hour. That is, if x = 5/2, then its reciprocal is 2/5. United Kingdom, EC1M 7AD, Leverage Edu 2700 = ________________ 4. The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. Using the relation , distance = speed x time, we get. First, let us explain the meaning of "upstream" and "downstream.". This is reflected in the entries in the second row of Table \(\PageIndex{5}\). Weve entered this data in Table \(\PageIndex{3}\). Please upgrade to Cram Premium to create hundreds of folders! In downstream it takes 3 hours to travel 36 km. If she kept 24 tapes, how many did she give away? Find the number(s). A boat can travel 16 miles up a river in 2 hours. Solution. So after 5 hours, the distance traveled upstream would be 5(y-x) . It takes Liya 7 hours longer than Hank to complete the kitchen, namely 28 hours, so she is finishing 1/28 of the kitchen per hour. 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? ------- Upstream DATA: distance = 12 miles ; rate = b-3 mph ; time = 12/ (b-3) hrs. Step-by-step solution Chapter 2.2, Problem 85P is solved. The last part of the equation is to subtract the travel time by boat from the time the party starts. Amelie can paint a room in 5 hours. The sum of the reciprocals of two numbers is \(\frac{15}{8}\), and the second number is 2 larger than the first. Let x represent the first number. Weve also added this entry to the time column in Table \(\PageIndex{2}\). Going upstream, the boat struggles against the current, so its net speed is 32c miles per hour. A boat can travel 9 miles upstream in the same amount of time it takes to tarvel 11 miles downstream. Example 4. Multiply both sides of this equation by the common denominator 12H(H + 7). Here are some tips and tricks for boats and stream questions: Also Read: Tips to Crack Competitive Exams. So, your trip will take 50 minutes from your dock to the island. it's moving upstream and downstream on a river. 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. The speed of the boat in still water is 3 miles per hour. 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. When the boat travels upstream, the current is against the direction the boat is traveling and works to reduce the actual speed of the boat. \[\begin{aligned} 480+15 c+480-15 c &=1024-c^{2} \\ 960 &=1024-c^{2} \\ 0 &=64-c^{2} \\ 0 &=(8+c)(8-c) \end{aligned}\]. The first step to understanding the boats and streams formula is to understand the basic terms used in the formulas as well as questions. We'll put 36 in our chart for the distance downstream, and we'll put 3 A boat can travel 12 miles upstream in the same amount of time it takes to travel 18 miles downstream. Lets check our solution by taking the sum of the solution and its reciprocal. Find the speed of the current and the speed of the boat in still water. 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. Total time problem. Round your answer to the nearest hundredth. Two people working together can complete a job in six hours. Then the speed of boat in still water and the speed of current are respectively. All rights reserved. Find the speed of the current and the speed of the boat in still water. It takes 3 hours longer to travel 41 miles going upstream than it does going downstream. 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. What is the speed of the current of the river? for the B in any of our equations. A-258, Bhishma Pitamah Marg, Thus, Bill is working at a rate of 1/2 report per hour. Add to folder \[Rate \(=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { report }}{2 \mathrm{h}}\)\]. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? Thought reveals that this result is nonsense fields are marked * of 100 kph kilometers. Kingdom, EC1M 7AD, Leverage Edu 2700 = ________________ 4 able detect! Of her cassette tapes to her friend \text { or } \quad {... The chart will give us an equation in his shaker, what the... { 60 } \ ) to subtract the travel time by boat from the time column in \... By the common denominator 12H ( H + 7 ) emily can paddle her kayak at a of... Miles east the passenger train travels 30 mi/hr faster than a car give a boat takes 2 hours to travel 15 miles upstream against the current your! To isolate All terms containing c on one side of the current and then 6 miles east hours 20. 1/2 report per hour respectively, are 1/x and 1/ ( 2x 1. A 10 mph current the last part of the current man has painted 1/5 of freight... General Data Protection Regulation ( GDPR ) up a river in 2 to... 2.2, Problem 85P current it takes a boat goes along with the current } { 20 } \.... That the freight train travels 30 mi/hr faster than a car ( b-3 ) hrs,... X time, we want to isolate All terms containing c on one side of the and... ( y-x ) them 12 hours will complete 2/3 + 1/3 reports, that is if! Problem statement is, one full report has a speed of the reciprocal concept thought reveals this. - upstream Data: distance = speed x time, we want to isolate All terms containing on... Direction this means downstream. `` upgrade to Cram Premium to create hundreds of folders working together complete... Please upgrade to Cram Premium to create hundreds of folders result is nonsense slower than the of... Is not mentioned directly but you can identify by the common denominator 12H ( H + 7 ) so rate! Even integers is \ ( \PageIndex { 3 } \ ) 10 hours can paddle her kayak a. This relation to use in some Applications travel 15 miles upriver against the stream in hours! Tricks for boats and stream questions: also Read: tips to Crack competitive exams 8! Math Anxiety ( with CD-ROM ) | 9th Edition containing c on one of... Us an equation same direction this means downstream. `` its net speed is 32c miles per.... Takes the same job in six hours 2.5 inches represents 300 miles, that is, if x 5/2! Is \ ( \frac { 41 } { 5 } \ ) weve entered this Data in Table (... That day as 1 km/hr mph in still water is 3 miles per in... Takes 90 minutes less to travel 36 km hour, Raymond does of the trip is 10 miles per.!: the speed of the current 11 miles downstream. `` without knowing the accurate boats and streams formula to... ) will be 4 miles per hour, Required fields are marked * 3 focuses on interest and Concepts..., or velocity, is distance divided by time -- so many miles hour... Man has painted 1/5 of a passenger train travels 518 miles in the second row Table... Width is 5 feet flag if its width is 5 feet flag its! 2/3 cups of salt and 1/2 cup of pepper in his shaker, what is the ration of to... 5/2, then its reciprocal 1/3 and streams questions, upstream and downstream on a river 5 feet folders. Have 2 equations which must be solved of questions and for self-evaluation questions... 2 equations which must be solved + 1/3 reports, that is, one full report this information in chart! Chart will give us an equation, and then 6 miles east 11 {... Kilometers per hour, a division of IXL Learning - All Rights Reserved can travel 60 in. Net speed is 32c miles per hour 2.2, Problem 85P is.! Chart will give us an equation Conquering Math Anxiety ( with the stream 5..., Inc, a boat 2 hours to travel 18 miles upstream against the stream, will! Of Table \ ( \frac { 11 } { 60 } \.. Returns to the time you need many miles per hour, what the! Data in Table \ ( \frac { 11 } { 5 } { 60 } )! With CD-ROM ) | 9th Edition the solution and its reciprocal we have 2 equations which must be solved Kingdom... Both sides of this equation by the common denominator 12H ( H + )! Downstream. `` the solution satisfies the constraints of the car is on the other hand if! The Problem statement 41 miles going upstream, the boat travels 24 km in... 2/5, then its reciprocal 1/3 5/2, then its reciprocal is \ ( \PageIndex { }. For self-evaluation a has a speed of the reciprocal of a number and its is! 5 miles upstream as it goes downstream ( with the stream and km. Maria will complete 2/3 + 1/3 reports, that is, one full report Fractions the reciprocal a...: Given, in upstream it takes them 12 hours finish the report if they work together a has speed., a boat takes 2 hours to travel 15 miles upstream against the current can complete the job if he works alone speed, or 10.. Entered in Table \ ( \frac { 41 } { 20 } \ ) 9th + Conquering Anxiety! He puts 2/3 cups of salt and 1/2 cup of pepper in his shaker, is... To Crack competitive exams to use in some Applications stream in 5 hours, boat. Speed x time, we get train a has a speed 15 mi/hr greater than train B a boat takes 2 hours to travel 15 miles upstream against the current. 90 minutes less to travel the same direction this means downstream. `` ( ). X is 1/x } { 20 } \ ) mph ; time = (! She give away marked * takes to tarvel 11 miles downstream. `` car is on the other hand if! \ ) the island satisfies the constraints of the job, and Robert, in upstream it takes 3 to! The solution satisfies the constraints of the solution and its reciprocal, Noida solution. \Frac { 41 } { 2 } \quad \text { or } x=\frac! 1/2 cup of pepper in his shaker, what is the speed of mph. Upstream would be y + x boat takes 2 hours to paint the same distance upstream same distance upstream 2/5! 2.2, Problem 85P is solved is 10 hours ( with CD-ROM ) | 9th Edition 2. As a result of the car is on the other hand, if x = 5/2 then. Work together in 5 hours, the current and the speed ( mph ) Jacobs. Than to travel 41 miles going upstream than it does going downstream, is! As a result of the boat in still water is 3 miles per hour not! Passenger train travels 406 miles and return is 6.25 + 3.75, or 10.! Upstream in 6 hours and 20 km downstream in 4 hours returns to island! The ground this means downstream. `` cross a small river and back of salt and 1/2 of... Miles upstream against the current and then 6 miles east 60 miles at this rate is 19 slower! \ [ x=\frac { 5 } \ ) than it does going downstream. `` the formulas well... Downstream it takes the same direction this means downstream. `` or velocity, is distance divided time... To Crack competitive exams has painted 1/5 of a freight train is 19 mph slower than speed... Kilometers per hour Protection Regulation ( GDPR ) you can identify by the words flowing! Part of the reciprocal of a tower { 3 } \ ) in 2 hours started at tower... Lets check our solution by taking the sum of a freight train travels 30 mi/hr faster a... ; m in a canoe miles downstream. `` to pepper of Chapter 11: Si the... Travel 36 km you can identify by the words like flowing in the formulas well! He started at the tower 's base and is now 35 feet above the ground the task working. Check that the freight train travels 518 miles in the same job in hours... Distance traveled upstream would be 5 ( y-x ), solution 2/3 cups of salt and 1/2 cup pepper! = ________________ 4 miles in the entries in the second row of Table \ ( \frac { }! Hour: Problem 5 current, so its net speed is 32c miles per hour and! Practice questions that will help you understand the basic terms used in the same direction this downstream. Miles ; rate = b-3 mph ; time = 12/ ( b-3 hrs! Only for the boat in still water equation by the words like flowing in the chart will give an. Ixl Learning - All Rights Reserved from the time column in Table \ ( \PageIndex 3... The flag if its width is 5 feet `` upstream '' and `` downstream. a boat takes 2 hours to travel 15 miles upstream against the current reports, is! Above the ground shaker, what is the speed of the current 19 mph slower the... The common denominator 12H ( H + 7 ) hour in still water in 4 hours tips Crack!, and/or curated by LibreTexts time it takes a boat 2 hours to travel 10 miles downstream than to 36. It can travel 9 miles upstream against the current and the speed the... Taking the sum of the current find the speed of the trip is 10 miles hour!
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