Two pipes A and B fill a swimming pool at constant rates of 10 gallons per minute and 15 gallons per minute respectively. The pool can be filled in 60 hours if Pipe A alone is left open or 40 hours if Pipe B alone is left open or 24 hours if both pipes are left open. If pipe B alone is used for half of the time to fill the pool and then both the pipes are used for remaining time, how many hours does it take to fill the pool?

A. 15
B. 30
C. 38.7
D. 42
E. 50


OA

chetan2u why did you equate it to 1

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We see that the capacity of the pool is 10 x 60 = 600 (or 15 x 40 = 600) gallons. If pipe B is used for half the time to fill the pool, we can let n = the time, in hours, pipe A has filled the pool after pipe B has filled the pool for the same amount of time, thus pipe B’s time = 2n and we can create the equation:

15(2n) + 10n = 600

40n = 600

n = 15

So the total time is 2 x 15 = 30 hours.

Answer: B
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Two pipes A and B fill a swimming pool at constant rates of 10 gallons per minute and 15 gallons per minute respectively. The pool can be filled in 60 hours if Pipe A alone is left open or 40 hours if Pipe B alone is left open or 24 hours if both pipes are left open. If pipe B alone is used for half of the time to fill the pool and then both the pipes are used for remaining time, how many hours does it take to fill the pool?

A. 15
B. 30
C. 38.7
D. 42
E. 50

let t=hours to fill pool
t/2*(1/40+1/24)=1➡
t=30 hours
B