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? 
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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
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Solving x:
x(1/8 + 1/10) = .75
Multiply both sides by 80:
x(10 + 8) = 60
18x = 60
x = 60/18 = 10/3
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Solving y:
y(1/10) = .25
y = 2.5 = 5/2
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Adding the two together:
10/3 + 5/2
= 20/6 + 15/6
= 35/6 hours