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Question 1163885: Pump A can fill a tank in 6 hours. Pump B can empty
the same tank in 10 hours. How long will it take both
pumps working together to fill the tank?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! A fills the tank in 6 hours
B empties the tank in 10 hours.
rate * time = quantity
time is in hours.
quantity is 1 tank
rate = quantity divided by time.
for pump A, the formula becomes rate * 6 = 1.
solve for rate to get pump A rate = 1/6 of the tank is filled each hour.
for pump B, the formula gecomew rate * 10 = 1.
solve for rate to get pump B rate = 1/10 of the tank is emptied each hour.
when one pump is working to fill the tank and one pump is working to empty the tank, their rates are subtractive.
if they were both working together to fill the tank, their rates would be additive.
the formula is therefore (rate A minus rate B) * time = 1
this formula becomes (1/6 minus 1/10) * time = 1
simplify to get (10/60 minus 6/60) * time = 1
combine like terms to get 4/60 * time = 1
solve for time to get time = 60/4 = 15 hours.
in 15 hours, pump A has filled 1/6 * 15 = 15/6 tanks.
in 15 hours, pump B has emptied 1/10 * 15 = 15/10 tanks.
15/6 minus 15/10 = 150/60 minus 90/60 = 60/60 = 1 tank.
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