a boat takes 2 hours to travel 15 miles upstream against the currenta boat takes 2 hours to travel 15 miles upstream against the current

What is the speed of the current? Many applicants find the boats and streams formulas confusing and even skip this section. A hiker follows a trail that goes from camp to lake. Your contact details will not be published. How many hours will it take if they work together? Find the rate of the current and the rate of the boat in still water. The sum of the reciprocals of two consecutive integers is \(\frac{19}{90}\). 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. \[\frac{1}{x}+\frac{1}{2 x+1}=\frac{7}{10}\]. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. How many hours would it take Amelie if she worked alone? It takes Maria 4 hours to complete 1 report. upstream, the current (which is C miles per hour) will be pushing against Lesson Plan Lets put this relation to use in some applications. A speedboat can travel 32 miles per hour in still water. Still Water- When the water is stationary i.e. Example 4. Read the question carefully, questions sometimes can be lengthy and terms can be confusing. to work with: The speed of the current is 2 miles per hour. However, as we saw above, the rates at which they are working will add. End-to-end support for your study abroad journey. Here are the important terms every applicant should know: Also Read: Permutation And Combination For Competitive Exams. Let x be how long will it take them if they work together. For example, in the first row, d = 60 miles and v = 3 c miles per hour. Jon P. It takes Jean 15 hours longer to complete an inventory report than it takes Sanjay. Suppose that he can canoe 4 miles upstream in the same amount of time as it takes him to canoe 8 miles downstream. We weren't able to detect the audio language on your flashcards. If the second number is 1 larger than twice the first number, then the second number can be represented by the expression 2x + 1. Note that we simply invert the number 3 to obtain its reciprocal 1/3. Note that the right-hand side of this equation is quadratic with ac = (14)(10) = 140. Here is the guiding principle. A student gave 2/3 of her cassette tapes to her friend. Boris can paddle his kayak at a speed of 6 mph in still water. It takes you the same amount of time to travel 15 miles downstream, with the current, as 9 miles upstream, against the current. Hence, we have two solutions for x. 2700 = ________________ 4. Thus. Katrina drove her car to Boston at a speed of 100 kph (kilometers per hour). Therefore, the sum of their reciprocals can be represented by the rational expression 1/x + 1/(2x + 1). .85 x 60 (minuntes in 1 hour) = 50 minutes. If Rajiv rows at his usual rate, he can travel 12 miles downstream in a . 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. \[\text { Rate }=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { kitchen }}{H \text { hour }}\]. We know that Bill does 1/2 reports per hour. Job problem. All rights reserved. Ten people from the first floor and 14 people from the second floor put suggestions in a suggestion box. A boat can travel 12 miles upstream in the same amount of time it takes to travel 18 miles downstream. Find the number(s). Solution : Speed of the boat in still water = 30 km/hr. The sum of a number and twice its reciprocal is \(\frac{9}{2}\). The integer pair {4, 21} has product 84 and sums to 17. The return trip takes2. hours going downstream. 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). This last equation is nonlinear, so make one side zero by subtracting 24H and 84 from both sides of the equation. Choose an expert and meet online. What is the rate of the boat in still water and what is the rate of the current? 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 \(\PageIndex{1}\)). Moira can paddle her kayak at a speed of 2 mph in still water. Below is the equation to convert this number into minutes. The passenger train travels 544 miles in the same time that the freight train travels 392 miles. Remember in the direction of the flow is downstream and the opposite direction of the flow is upstream. What are we trying to find in this problem? 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. Weve also added this entry to the time column in Table \(\PageIndex{2}\). Dont let it confuse you. where d represents the distance traveled, v represents the speed, and t represents the time of travel. Find the speed of the current and the speed of the boat in still water. 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. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. it will become 12 = B+C. {\(\frac{2}{3}\), \(\frac{8}{3}\)} and {\(\frac{8}{5}\), \(\frac{2}{5}\)}. 19 . { "3.17.01:_Introducing_Rational_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.17.02:_Reducing_Rational_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.17.03:_Graphing_Rational_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.17.04:_Products_and_Quotients_of_Rational_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.17.05:_Sums_and_Differences_of_Rational_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", 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If the speed of the boat in still water is 10 mph, the speed of the stream is: document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); 150 Common: Difficult Idioms with Examples. The speed of the boat (in still water) is 13 miles/hour. (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 the rate of the boat in still water is 13 miles per hour what is the rate of the - 20218675 What is the speed (in mph) of the current? Break up the middle term using this pair and factor by grouping. This leads to the result, \[\frac{60}{3-c}=2\left(\frac{60}{3+c}\right)\]. d = rt, and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream. | CE Board Problem in Mathematics, Surveying and Transportation Engineering Home Date of Exam: November 2018 Subject: In this direction, the current works WITH the boat's engine, so the rate would be y + x. If train A travels 150 miles in the same time train B travels 120 miles, what are the speeds of the two trains? The speed of the current is miles per hour. CH2.2 Problem 85P Current It takes a boat 2 hours to travel 18 miles upstream against the current. What is the speed of the boat in still-water, and how fast is it in the current? Hence, the sum of x and its reciprocal is represented by the rational expression x + 1/x. Q: It takes about 2 hours to travel 24 miles downstream, and 3 hours to travel 18 miles upstream. It takes Amelie 10 hours to paint the same room. Uttar Pradesh 201301, Devonshire House, 60 Goswell Road, Find the two numbers. of two equations to solve. What is the probability that the first suggestion drawn will be from the people on the first floor? Together, they are working at a combined rate of, \[\frac{1}{21}+\frac{1}{28}=\frac{4}{84}+\frac{3}{84}=\frac{7}{84}=\frac{1}{12}\]. But the boat is not on a still lake; 2281 . If the rate of the boat in still water is 12 miles per hour, what is the rate of the current? Let x be the distance to Boston. 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? The length of a flag is 1.9 times its width. 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. The speed of the current is 5 miles per hour. as required by the problem statement. Based on the equation, it will take you .85 hours to get to the island party. Then the speed of the car is 4(b - c) = 128. Leverage Edu Tower, Boats and stream questions are a common topic in the quantitative aptitude section of government exams such as SSC, UPSC, BANK PO, and entrance exams like CAT, XAT, MAT, etc. Solution. 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. That is, if x = 5/2, then its reciprocal is 2/5. A train travels 30 mi/hr faster than a car. The boat travels at miles per hour in still water. The speed of a freight train is 19 mph slower than the speed of a passenger train. A boat travels 30 miles upstream in 5 hours. It takes the same time for the boat to travel 5 miles upstream as it does to travel 10 miles downstream. We know that if the boat were on a still lake, its motor would propel it \[\begin{aligned}\color{blue}{(32-c)(32+c)}\left(\frac{150}{32-c}+\frac{150}{32+c}\right) &=10\color{blue}{(32-c)(32+c)} \\ 150(32+c)+150(32-c) &=10\left(1024-c^{2}\right) \end{aligned}\]. United Kingdom, EC1M 7AD, Leverage Edu If the current of the river is 3miles per hour, complete the chart below and use it to find the speed of the boat in still water. How many hours will it take if they work together? Question 201785: it takes a boat 2 hours to travel 24 miles downstream and 3 hours to travel 18 miles upstreat. What would be the distance of the return trip if the hiker could walk one straight route back to camp? 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 Liya 7 more hours to paint a kitchen than it takes Hank to complete the same job. x30. When a boat travels against the current, it travels upstream. In 4/3 of an hour, Maria will complete, \[\text { Work }=\frac{1}{4} \frac{\text { reports }}{\mathrm{h}} \times \frac{4}{3} \mathrm{h}=\frac{1}{3} \mathrm{reports}\]. The rate of the current is 15 km/hour and the . It takes Bill 2 hours to complete 1 report. 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 For Free. The speed of a boat in still water is 30 mph. Again, it is very important that we check this result. The speed of a boat in still water is 15 mi/hr. Introducing Cram Folders! What was the interest rate on the loan? 2003-2023 Chegg Inc. All rights reserved. Hence, the pair {14/5, 7/2} is also a solution. This is an alternate ISBN. He paddles 5 miles upstream against the current and then returns to the starting location. \[\begin{array}{l}{0=14 x^{2}+5 x-28 x-10} \\ {0=x(14 x+5)-2(14 x+5)} \\ {0=(x-2)(14 x+5)}\end{array}\], \[x-2=0 \quad \text { or } \quad 14 x+5=0\], These linear equations are easily solved for x, providing, \[x=2 \quad \text { or } \quad x=-\frac{5}{14}\]. Please sign in to share these flashcards. The speed of a freight train is 16 mph slower than the speed of a passenger train. What proportion of the kites are blue? The sum of the reciprocals of two consecutive odd integers is \(\frac{28}{195}\). A common misconception is that the times add in this case. To set up an equation, we need to use the fact that the time to travel upstream is twice the time to travel downstream. We'll put 36 in our chart for the distance downstream, and we'll put 3 We'll put this information in our chart: Each row in the chart will give us an equation. A boat takes 2 hours to travel 15 miles upriver against the current. a. She paddles 5 miles upstream against the current and then returns to the starting location. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes . 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. The speed of the boat (b) in still water is 10 miles/hour and the rate of the current (c) is 8 miles/hour. So now we have a second equation: 2(y+x) = 100. 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 . by Martynabucytram11, 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. that distance. How many miles are represented by 6 inches? How many hours would it take Sanjay if he worked alone? Jacob can paddle his kayak at a speed of 6 mph in still water. 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning. The hiker walks 8 miles north, and then 6 miles east. If they work together, it takes them 8 hours. Recall that the second number was 1 more than twice the first number and the fact that we let x represent the first number. Dec. 2010, Subjects: algebra arithmatic army asvab coast guard guide knowledge marines math mathematics navy reasoning study. Then. A boat can travel 24 miles in 3 hours when traveling with a current. Note that each row of Table \(\PageIndex{1}\) has two entries entered. Maria can finish the same report in 4 hours. To cover the answer again, click "Refresh" ("Reload").But do the problem yourself first! it's moving upstream and downstream on a river. How long will it take them to finish the report if they work together? That is, \[a \cdot \frac{1}{a}=1\], For example, the reciprocal of the number 3 is 1/3. 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 numbers is \(\frac{16}{15}\), and the second number is 1 larger than the first. What are the speed of the boat in still water and the speed of the stream? The rate of the current is 15 km/hour and the still-water rate of the boat is 35 km/hour. Block A, Defence Colony, New Delhi, . It takes Sanjay 9 hours to paint the same room. The resulting speed of the boat (traveling downstream)

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