AAPL wrote:Manhattan Prep

Two hoses are pouring water into an empty pool. Hose 1 alone would fill up the pool in 6 hours. Hose 2 alone would fill up the pool in 4 hours. How long would it take for both hoses to fill up two-thirds of the pool?

A. 5/12 hours
B. 5/8 hours
C. 8/5 hours
D. 12/7 hours
E. 12/5 hours

OA C

We see that the rate of hose 1 is 1/6, and the rate of hose 2 is 1/4. We can let x = time needed to fill 2/3 of a pool when they work together and create the equation:

1/6(x) + 1/4(x) = 2/3

Multiplying the equation by 12, we have:

2x + 3x = 8

5x = 8

x = 8/5 hours

Answer: C

Hi All,

This question is a variation of a 'Work Formula' question (it involves 2 'entities' working on the same task together), so we can use the Work Formula to solve it.

Work = (A)(B)/(A+B) where A and B are the individual times that it takes the 2 entities to complete the task on their own.

Here, we're told that Hose 1 can fill a pool in 6 hours and that Hose 2 can fill the pool in 4 hours. We're asked how long it takes the two hoses to fill 2/3 of the pool...

To fill the ENTIRE POOL, it takes...

(6)(4)/(6+4) = 24/10 = 2.4 hours

To fill 2/3 of the pool takes 2/3 of the time. Since 2.4 hours = 12/5 hours, it would take...

(2/3)(12/5) = 24/15 = 8/5 hours to fill 2/3 of the pool.

Final Answer: C

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