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.