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Question 252292: Working alone, pump A can fill a pool in 8 hours, while pump B can fill it in 10 hours. The two pumps are turned on at the same time and run until the pool is 75% full. Pump A then stops working, but pump B continues until the pool is filled. How long does it take to fill the empty pool?
a 10/3 hours b 16/3 hours c 23/6 hours d 29/6 hours e 35/6 hours
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Working alone, pump A can fill a pool in 8 hours, while pump B can fill it in 10 hours. The two pumps are turned on at the same time and run until the pool is 75% full. Pump A then stops working, but pump B continues until the pool is filled. How long does it take to fill the empty pool?
.
Let x = time pumps ran when filling to 75%
and y = time pump B ran to complete filling the pool
then
x(1/8 + 1/10) = .75
y(1/10) = .25
.
Solving x:
x(1/8 + 1/10) = .75
Multiply both sides by 80:
x(10 + 8) = 60
18x = 60
x = 60/18 = 10/3
.
Solving y:
y(1/10) = .25
y = 2.5 = 5/2
.
Adding the two together:
10/3 + 5/2
= 20/6 + 15/6
= 35/6 hours
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