SOLUTION: a 5 horsepower (hp) pump can empty a pool in 5 hours. a smaller, 2 hp pump empties the same pool in 8 hours. the pumps are used together to begin emptying this pool. after 2 hours,

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Question 167649: a 5 horsepower (hp) pump can empty a pool in 5 hours. a smaller, 2 hp pump empties the same pool in 8 hours. the pumps are used together to begin emptying this pool. after 2 hours, the 2 hp pump breaks down. how long will it take the larger pump to finish emptying the pool? --- i get that for the entire time, minus the 2hp pump breaking down, the equation would be 1/5+1/8=1/t, 8t+5t=40, 13t=40, t=40/13=3.08hours... but i do not know how to take into consideration the 2hp pump breaking down. any help would be much appreciated!

Answer by stanbon(57424) About Me  (Show Source):
You can put this solution on YOUR website!
a 5 horsepower (hp) pump can empty a pool in 5 hours. a smaller, 2 hp pump empties the same pool in 8 hours. the pumps are used together to begin emptying this pool. after 2 hours, the 2 hp pump breaks down. how long will it take the larger pump to finish emptying the pool?
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5 hp pump DATA:
time = 5 hrs/job ; rate = 1/5 job/hr
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2 hp pump DATA:
time = 8 hrs/job ; rate = 1/8 job/hr
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In two hours working together,
2(1/5 + 1/8) = 2(13/40) = 13/20 of the job is done.
That leaves 7/20 of the job to be done by the 5 horsepower pump.
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Let time for the 5 hp to finish the job be "x" hrs.
x(1/5) = 7/20
x = 7/4 hr = 1 3/4 hr. = 1 hr. 45 minutes
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Cheers,
Stan H.