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Working together at their respective rates, two hoses fill a pool in 2 [#permalink]
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08 Aug 2017, 01:22
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Re: Working together at their respective rates, two hoses fill a pool in 2 [#permalink]
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08 Aug 2017, 01:35
Bunuel wrote: Working together at their respective rates, two hoses fill a pool in 2 hours. If one of the hoses, working alone, could fill the pool in 3 hours, how long would it take the other hose to fill the pool alone?
A. 2 hours B. 3 hours C. 4 hours D. 5 hours E. 6 hours Let the hoses be \(A\) and \(B\). Given \(A\) and \(B\) hoses together can fill a pool in \(2\) hours. Therefore \(1\) hour work of \(A\) and \(B\) together is equal to. \(\frac{1}{A} + \frac{1}{B} = \frac{1}{2}\) Given \(A\) could fill the pool in \(3\) hours alone. Therefore, \(A = 3\) hours \(\frac{1}{3} + \frac{1}{B} = \frac{1}{2}\) \(\frac{1}{B} = \frac{1}{2}  \frac{1}{3} = \frac{32}{6} = \frac{1}{6}\) \(B = 6\) hours Therefore \(B\) can fill the pool alone in \(6\) hours. Answer (E)...



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Re: Working together at their respective rates, two hoses fill a pool in 2 [#permalink]
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08 Aug 2017, 01:37
Bunuel wrote: Working together at their respective rates, two hoses fill a pool in 2 hours. If one of the hoses, working alone, could fill the pool in 3 hours, how long would it take the other hose to fill the pool alone?
A. 2 hours B. 3 hours C. 4 hours D. 5 hours E. 6 hours Pool is 6 units Hose A + Hose B = 3 units/hr Hose A = 2 units/hr Hose B = 1 unit/hr Time = 6/1 = 6 hrs E
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Re: Working together at their respective rates, two hoses fill a pool in 2 [#permalink]
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04 Dec 2017, 14:40
Hi All, This question is a standard example of a Work Formula question (with 2 'entities' working on a job together). When this type of question has no 'quirks' to it (such as 3 or more entities or one of the entities stops working partway through the job), you can use the Work Formula to answer it: Work = (A)(B)/(A+B) = amount of time to complete the job while working together (where A and B are the two individual times it takes to do the job). In this prompt, we know that one of the hoses takes 3 hours to do the job alone and that the two hoses (working together) can complete the job in 2 hours.... (3)(B)/(3+B) = 2 hours 3B = (2)(3+B) 3B = 6 + 2B B = 6 hours Thus, it would take the second hose 6 hours to fill the pool by itself. Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: Working together at their respective rates, two hoses fill a pool in 2 [#permalink]
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04 Jan 2018, 11:12
Bunuel wrote: Working together at their respective rates, two hoses fill a pool in 2 hours. If one of the hoses, working alone, could fill the pool in 3 hours, how long would it take the other hose to fill the pool alone?
A. 2 hours B. 3 hours C. 4 hours D. 5 hours E. 6 hours We can let n = the time, in hours, it takes the other hose to fill the pool alone. Thus, the rate of that hose = 1/n. Since the rate of the known hose = 1/3 and the combined rate = 1/2, we have: 1/n + 1/3 = 1/2 Multiplying by 6n, we have: 6 + 2n = 3n 6 = n Thus, the other hose takes 6 hours to fill the pool. Answer: E
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Working together at their respective rates, two hoses fill a pool in 2 [#permalink]
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04 Jan 2018, 13:43
Bunuel wrote: Working together at their respective rates, two hoses fill a pool in 2 hours. If one of the hoses, working alone, could fill the pool in 3 hours, how long would it take the other hose to fill the pool alone?
A. 2 hours B. 3 hours C. 4 hours D. 5 hours E. 6 hours Since one of the hoses fills the pool in 3 hours and both the hoses fill the pool in 2 hour, we should assume a number divisible by both these numbers to be the total capacity of the pool. Let that be 60 units. Let the hose which can fill the pool alone in 3 hours be hose A, so the rate of work is 20 units/hour. Similarly, both the hoses can fill the pool in 2 hours, and must fill 30 units/hour. Hence, the other hose must be filling the pool at the rate of 10 units/hr Therefore, the time taken to fill the entire pool is \(\frac{60}{10}\) (6 hours  Option E)
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Re: Working together at their respective rates, two hoses fill a pool in 2 [#permalink]
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10 Jan 2018, 08:26
Bunuel wrote: Working together at their respective rates, two hoses fill a pool in 2 hours. If one of the hoses, working alone, could fill the pool in 3 hours, how long would it take the other hose to fill the pool alone?
A. 2 hours B. 3 hours C. 4 hours D. 5 hours E. 6 hours Another approach is to assign a nice value to the job. In this case, we need a value that works well with the given information (2 hours and 3 hours). So, let's say the job consists of filling a pool containing 6 liters of water One of the hoses, working alone, takes 3 hours to fill the pool We'll call this hose A. Let A = the rate of work of this hose If it takes 3 hours for this hose to fill a 6liter pool, then.... A = 6/3 = 2 liters per hour (since rate = output/time) Working together at their respective rates, two hoses fill a pool in 2 hours. Let B = the rate of work of the other hose So, the COMBINED rate = A+B If it takes 2 hours for the combined hoses to fill a 6liter pool then.... A+B = 6/2 = 3 liters per hour (since rate = output/time) So, if A = 2 liters per hour, and A+B = 3 liters per hour Then we can see that B = 1 liter per hour How long would it take the other hose (hose B) to fill the pool alone? Time = output/rate = 6/ 1 = 6 hours Answer: E Cheers, Brent
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Re: Working together at their respective rates, two hoses fill a pool in 2 [#permalink]
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10 Jan 2018, 09:03
Bunuel wrote: Working together at their respective rates, two hoses fill a pool in 2 hours. If one of the hoses, working alone, could fill the pool in 3 hours, how long would it take the other hose to fill the pool alone?
A. 2 hours B. 3 hours C. 4 hours D. 5 hours E. 6 hours Let the total capacity of the pool be 6 units Efficiency of A + B = 3 units/hr Efficiency of B = 2 units/hr So, Efficiency of A = 1 unit/hr Thus, time required to fill the pool alone is 6 hours, answer will be (E)
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Re: Working together at their respective rates, two hoses fill a pool in 2
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