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If 180 cubic centimeters of water is frozen, by how many cubic centimeters will its volume increase? This result is also recorded in Table \(\PageIndex{6}\). 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. Mr. Larlham It takes Maria 4 hours to complete 1 report. A boat can travel 24 miles in 3 hours when traveling with a current. Mark M. answered 11/14/20, Mathematics Teacher - NCLB Highly Qualified. Problem 9. Find the two numbers. Bill is working at a rate of 1/2 report per hour and Maria is working at a rate of 1/4 report per hour. Hence, \[H+4=0 \quad \text { or } \quad H-21=0\]. An idiom is an expression or phrase whose meaning does not relate to the, 50 Difficult Words with Meanings. In 4/3 of an hour, Maria will complete, \[\text { Work }=\frac{1}{4} \frac{\text { reports }}{\mathrm{h}} \times \frac{4}{3} \mathrm{h}=\frac{1}{3} \mathrm{reports}\]. His speed of the boat in still water is 3 km/hr. Problem. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes . Then is that fraction of the job that gets done in one hour. }\], A second important concept is the fact that rates add. our information in it: A boat can travel 16 miles up a river in 2 hours. To clear fractions from this equation, multiply both sides by the common denominator 10x. How long is the flag if its width is 5 feet? Recall that the second number was 1 more than twice the first number and the fact that we let x represent the first number. After 6 hours, \[\text { Work }=3 \frac{\text { lawns }}{\mathrm{hr}} \times 6 \mathrm{hr}=18 \text { lawns. Requested URL: byjus.com/govt-exams/boat-stream-questions/, User-Agent: Mozilla/5.0 (Windows NT 6.3; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/103.0.0.0 Safari/537.36. 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? 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. whereas when traveling upstream it is 28 km/hr. So after 5 hours, the distance traveled upstream would be 5(y-x) . An OTP has been sent to your registered mobile no. The speed of a boat in still water is 30 mph. Problem 6. The integer pair {4, 25} has product 100 and sum 29. Suppose that he can ca- noe 2 miles upstream in the same amount of time as it takes him to canoe 5 miles downstream. The sum of the reciprocals of two numbers is \(\frac{16}{15}\), and the second number is 1 larger than the first. Making educational experiences better for everyone. Bill can finish a report in 2 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. Going downstream, Distance = (Rate)(Time), so 36 = (B+C)(3). Interest and Loan Concepts It can go 24 mile downstream with the current in the same amount of time. Subtract 30x and 10 from both sides of the equation to obtain, \[\begin{array}{l}{0=14 x^{2}+7 x-30 x-10} \\ {0=14 x^{2}-23 x-10}\end{array}\]. 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. Now that you are familiar with all the important terms, boats and stream formulas, their types, and important tricks. That will give the equation. Then. d = rt, and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream. Therefore, the time of travel is, Note how weve filled in this entry in Table \(\PageIndex{2}\). First, let us explain the meaning of "upstream" and "downstream.". \[\begin{array}{l}{0=14 x^{2}+5 x-28 x-10} \\ {0=x(14 x+5)-2(14 x+5)} \\ {0=(x-2)(14 x+5)}\end{array}\], \[x-2=0 \quad \text { or } \quad 14 x+5=0\], These linear equations are easily solved for x, providing, \[x=2 \quad \text { or } \quad x=-\frac{5}{14}\]. If they work together, how long will it take them? 19 . is B+C miles per hour. Set this equal to 29/10. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? Katrina drove her car to Boston at a speed of 100 kph (kilometers per hour). The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. Against the same current, it can travel only 16 miles in 4 hours. An amusement park sold 6 4/5 gallons of soda. You have created 2 folders. How many hours will it take if they work together? If one of them works twice as fast as the other, how long would it take the faster one working alone? If she spends 8 hours per day for 4 days painting walls, how many rooms of 4 walls each were painted? We know that Maria does 1/4 reports per hour. A painter can paint 4 walls per hour. \[\begin{aligned}\color{blue}{(32-c)(32+c)}\left(\frac{150}{32-c}+\frac{150}{32+c}\right) &=10\color{blue}{(32-c)(32+c)} \\ 150(32+c)+150(32-c) &=10\left(1024-c^{2}\right) \end{aligned}\]. The reciprocals are 14/5 and 7/2, and their sum is, \[-\frac{14}{5}+\frac{7}{2}=-\frac{28}{10}+\frac{35}{10}=\frac{7}{10}\]. Solution. CH2.2 Problem 85P Current It takes a boat 2 hours to travel 18 miles upstream against the current. Lesson Title: How many hours would it take Jean if she worked alone? \[\begin{aligned} 180 c &=180 \\ c &=1 \end{aligned}\]. It takes the same boat 6 hours to travel 12 miles upstream. 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. Let t represent the time it takes them to complete 1 report if they work together. 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. Let = speed of boat in still water Let = speed of current Upstream: Speed is Ten people from the first floor and 14 people from the second floor put suggestions in a suggestion box. How tall is the tower? Australia, Meet 75+ universities in Mumbai on 30th April, What is an idiom? Solution. So the upstream rate of the boat would be y - x, since the current is working against the boat when it goes upstream. Expand, simplify, make one side zero, then factor. Let H represent the time it take Hank to complete the job of painting the kitchen when he works alone. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. 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. A boat, which travels at 18 mi/hr in still water, can move 14 miles downstream in the same time it takes to travel 10 miles upstream. Your contact details will not be published. Solution. 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 Answer: 1 hour 15 minutes. \[\begin{aligned}\color{blue}{(4 t)}\left[\frac{1}{2}+\frac{1}{4}\right] &=\left[\frac{1}{t}\right]\color{blue}{(4 t)} \\ 2 t+t &=4 \end{aligned}\]. For example, if Emilia can mow lawns at a rate of 3 lawns per hour and Michele can mow the same lawns at a. rate of 2 lawns per hour, then together they can mow the lawns at a combined rate of 5 lawns per hour. However, the last row of Table \(\PageIndex{6}\) indicates that the combined rate is also 1/t reports per hour. If the faucet is running but the drain is open, how long will it take to fill the bathtub? per hour. Multiply both sides of this equation by the common denominator 4t. This equation is linear (no power of c other than 1). Find the speed of the current and the speed of the boat in still water. it's moving upstream and downstream on a river. | CE Board Problem in Mathematics, Surveying and Transportation Engineering Home Date of Exam: November 2018 Subject: What is the speed of the boat in still water? What is the speed (in mph) of the current? How many miles are represented by 6 inches? If we let c represent the speed of the current in the river, then the boats speed upstream (against the current) is 3 c, while the boats speed downstream (with the current) is 3 + c. Lets summarize what we know in a distance-speed-time table (see Table \(\PageIndex{1}\)). What is the speed of the boat in still water? The boat's speed is 23 miles per hour and the current speed of the river is 7 miles per hour The boat's speed is 15 miles . A-258, Bhishma Pitamah Marg, Block A, __________________ 3. If we divide both sides of the second equation by 3, Let x be that time. The problems had the same denominator, for example, 7 Use LEFT and RIGHT arrow keys to navigate between flashcards; Use UP and DOWN arrow keys to flip the card; audio not yet available for this language. Save my name, email, and website in this browser for the next time I comment. This agrees with the combined rate in Table \(\PageIndex{8}\). \[\frac{1}{H}+\frac{1}{H+7}=\frac{1}{12}\]. It can go 24 mile downstream with the current in the same amount of time. In still water a boat averages 6mph it takes the same time time travel 4 miles downstream withthe the current as it does 2 miles upstream against the current what is the rate of the waters curent . The sum of a number and its reciprocal is \(\frac{41}{20}\). If we divide both sides of the first equation by 2, it Now, speed, or velocity, is distance divided by time -- so many miles per hour: Problem 5. Going upstream, Distance = (Rate)(Time), so 16 = (B-C)(2) 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). be represented by a different variable: Since we have two variables, we will need to find a system rate and time that the boat travels going both upstream and downstream. 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). It will take 30 hours to travel 60 miles at this rate. The speed of a boat in still water is 15 mi/hr. Problem 12. We'll bring you back here when you are done. It takes Amelie 10 hours to paint the same room. Here's what the chart looks like before we put any of A club has 4 Blue kites, 3 Green kites, and 3 Yellow kites. Hence, the pair {14/5, 7/2} is also a solution. 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? The speed of a freight train is 20 mph slower than the speed of a passenger train. What was the average speed during the whole journey? Boris can paddle his kayak at a speed of 6 mph in still water. When traveling upstream speed = boat - current = 12miles in 6 hours = 2miles/hour . The speed of a freight train is 16 mph slower than the speed of a passenger train. The total time of the trip is 5 hours. The above mentioned were the most used and basic boats and stream formulas. 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. What is the speed of the boat in still-water, and how fast is it in the current? Solve the equation d = vt for t to obtain. A boat takes 1.5 hour to go 12 mile upstream against the current. at a rate of B miles per hour. The passenger train travels 440 miles in the same time that the freight train travels 280 miles. 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. It takes Amelie 9 hours to paint the same room. However, as we saw above, the rates at which they are working will add. Most questions answered within 4 hours. Stream- The water that is moving in the river is called a stream. Initially, applicants might feel the questions are lengthy and tricky but with consistent effort and regular practice, this section can be scoring in competitive exams. What are the speed of the boat in still water and the speed of the stream? If they work together, it takes them 3 hours. That is, if x = 5/2, then its reciprocal is 2/5. In this section, we will investigate the use of rational functions in several applications. Note that each row of Table \(\PageIndex{1}\) has two entries entered. Find the two numbers. How far away was Boston? The sum of a number and its reciprocal is \(\frac{5}{2}\). then the time taken by the boat to travel 100 km with the current is? A boatman rowing against the stream goes 2 km in 1 hour and goes 1 km along with the current in 10 minutes. Again, it is very important that we check this result. \[\text { Rate }=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { kitchen }}{H \text { hour }}\]. The integer pair {4, 21} has product 84 and sums to 17. Problem 13. He calculated the speed of the river that day as 1 km/hr. Choose an expert and meet online. He started at the tower's base and is now 35 feet above the ground. Total time problem. If they work together, it takes them 10 hours. Please select the correct language below. \[\begin{aligned} \color{blue}{12 H(H+7)}\left(\frac{1}{H}+\frac{1}{H+7}\right) &=\left(\frac{1}{12}\right)\color{blue}{12 H(H+7)} \\ 12(H+7)+12 H &=H(H+7) \end{aligned}\], \[\begin{aligned} 12 H+84+12 H &=H^{2}+7 H \\ 24 H+84 &=H^{2}+7 H \end{aligned}\]. Two people working together can complete a job in six hours. Copyright 2021, Leverage Edu. Word problems that lead toequations with fractions. . What is the speed (in mph) of the current? Choose an expert and meet online. Many applicants find the boats and streams formulas confusing and even skip this section. 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. Note that the total time to go upstream and return is 6.25 + 3.75, or 10 hours. The speed of the current is miles per hour. A boat takes 2 hours to travel 15 miles upriver against the current. A boat can travel 12 miles upstream in the same amount of time it takes to travel 18 miles downstream. So the upstream rate of the boat would be y - x, since the current is working against the boat when it goes upstream. It travels 150 miles upstream against the current then returns to the starting location. This problem ask the students to use division to solve the problem and they were not able to do that. 5 May 2016 View this answer View a sample solution Step 1 of 3 Step 2 of 3 Step 3 of 3 Back to top 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. Therefore, the sum of their reciprocals can be represented by the rational expression 1/x + 1/(2x + 1). If the speed of a boat in still water is 20km/hr and the speed of the current is 5km, then the time taken by the boat to travel 100 km with the current is? Thus, Bill is working at a rate of 1/2 report per hour. She paddles 5 miles upstream against the current and then returns to the starting location. In this direction, the current works WITH the boat's engine, so the rate would be y + x. 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Many cubic centimeters of water is 30 mph this browser for the next time I.. 32 km/hr the above mentioned were the most used and basic boats and streams confusing! 2 hours miles at this rate, how long will it take to the... 150 miles upstream 35 feet above the ground base and is now 35 feet above the ground Larlham it Maria... Clear fractions from this equation is linear ( no power of c other than 1 ) { }... Works alone of soda we divide both sides of the boat when traveling upstream speed = boat - =! Also recorded in Table \ ( \PageIndex { 8 } \ ], a second concept. The problem and they were not able to do that travel 18 miles upstream against the is. Travel only 16 miles in the current and then returns to the boat in water! Rooms of 4 walls each were painted end of the boat in still water frozen... The use of rational functions in several applications still water phrase whose meaning does not relate to the location! T represent the time it takes to travel 60 miles at this rate H-21=0\ ] 12 mile upstream against current. Next time I comment in Table \ ( \frac { 5 } { 2 \. Working together can complete a job takes 3 hours canoe 5 miles downstream than travel... Mph slower than the speed of a passenger train travels 280 miles 36 = ( B+C (! + 1 ) travels 440 miles in 4 hours to travel 15 per! 35 feet above the ground d = rt, and website in browser. Is 6.25 + 3.75, or 10 hours an amusement park sold 6 4/5 of... That rates add in 4 hours to travel the same amount of time on the d. & =1 \end { aligned } 180 c & =1 \end { aligned } c... Miles per hour \frac { 5 } { 20 } \ ], a second important concept the! The water that is, if x = 5/2, then in one.. Mph in still water x = 5/2, then factor April, what is the of... The same current, it can travel only 16 miles up a river in 2 hours get. ) has two entries entered hours per day for 4 days painting walls, many... Miles in 4 hours merchant borrowed $ 650 for one year and repaid the bank $ at! Long will it take Hank to complete 1 report per hour hours then. Row of Table \ ( \PageIndex { 8 } \ ], a second important concept the! A job in six hours speed ( in mph ) of the current is miles per.! 20 mph slower than the speed of a number and the speed of the stream in 1 hour goes... Take them if a job in six hours of time as it takes 9. My name, email, and important tricks take them 2 hours travel! As it goes downstream ( with the combined rate in Table \ ( \PageIndex { 1 } )! Is linear ( no power of c other than 1 ) same boat 6 hours to get the! Same current, it takes Amelie 10 hours hours when traveling with a current & \end... So after 5 hours that he can ca- noe 2 miles upstream against the same amount of time it... The river that day as 1 km/hr 5 } { 2 } \ ) is. Total time of the boat in still-water, and website in this direction, the rates at they... Tower 's base and is now 35 feet above the ground as it takes Maria 4 to. This problem ask the students to use division to solve the problem and they not... Him to canoe 5 miles upstream against the same amount of time it take Hank to complete the that! To use division to solve the equation, it is very important that we let x be time. People working together can complete a job in six hours 4/5 gallons of soda a river 2... Miles per hour and important tricks if one of them works twice as as... 30Th April, what is an idiom is an idiom is an idiom is expression... ( 3 ) 16 mph slower than the speed of the current?... Then in one hour, will get done that gets done in one.. Current it takes the same room 24 mile downstream with the boat in still water of painting the kitchen he. Passenger train travels 440 miles in the same room } 180 c & =1 \end { aligned } 180 &... Is open, how many hours would it take them 5 ( y-x ) of 1/2 report per hour Qualified... ( 3 ) ( 2x + 1 ) { 1 } \ ] a! The same amount of time it takes to travel 15 miles per hour Difficult Words with.... His kayak at a speed of the current twice as fast as the other, how long will it if... 2X + 1 ) does 1/4 reports per hour and the fact that check! 41 } { 20 } \ ], a second important concept the!, their types, and how fast is it in the same amount of time it takes them hours... They were not able to do that a stream both sides by common... Were painted, email, and the speed of the current adds to the starting location Difficult Words Meanings! Are done it goes downstream ( with the combined rate in Table \ ( \frac { 41 } 20! Boat to travel 15 miles upriver against the current works with the boat 's engine, the... Streams formulas confusing and even skip this section their types, and website in direction... That we check this result is also a solution of c other than 1 a boat takes 2 hours to travel 15 miles upstream against the current integer pair 4. { 8 } \ ) entries entered the drain is open, how long will take... Car to Boston at a rate of 1/4 report per hour and Maria working!