AAPL wrote: ↑

Mon Mar 16, 2020 4:39 am

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

Given the information, Hose 1 would fill 1/6th of the pool in 1 hour and Hose 2 would fill 1/4th of the pool in 1 hour.

Thus, in 1 hour, both hoses would fill 1/6 + 1/4 = 5/12 part of the pool in 1 hour

Thus, the pool would be completely be filled in 12/5 hours;
Thus, two-thirds of the pool would be filled in 12/5*2/3 = 8/5 hours

The correct answer: C

Hope this helps!

-Jay
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AAPL wrote: ↑

Mon Mar 16, 2020 4:39 am

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