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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

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by GMATGuruNY » Wed Feb 27, 2019 3:29 am
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
Let the pool = 12 gallons.
Since Hose 1 takes 6 hours to fill the 12-gallon pool, the rate for Hose 1 = w/t = 12/6 = 2 gallons per hour.
Since Hose 2 takes 4 hours to fill the 12-gallon pool, the rate for Hose 2 = w/t = 12/4 = 3 gallons per hour.
Since the combined rate for the two hoses = 2+3 = 5 gallons per hour, the time to fill 2/3 of the 12-gallon pool = w/r = (2/3 * 12)/5 = 8/5 hours.

The correct answer is C.
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by swerve » Wed Feb 27, 2019 6:56 am
Time taken by H1 =6, W=1, R1=1/6
Time taken by H2=4, w=1, R2 =1/4
so together R1+R2 =1/6+1/4= 5/12
and
w=2/3, t = w/(R1+R2) = 2/3 *12/5 = 8/5

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by Scott@TargetTestPrep » Sat Mar 02, 2019 8:03 am
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

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by Rich.C@EMPOWERgmat.com » Sat Mar 02, 2019 1:18 pm
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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