SOLUTION: A large pump can fill a 10,000 gallon tank 5 hours faster than a small pump. The large pump outputs water 100 gallons per hour faster than the small pump. Find the number of gallon
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Question 323282: A large pump can fill a 10,000 gallon tank 5 hours faster than a small pump. The large pump outputs water 100 gallons per hour faster than the small pump. Find the number of gallons pumped in 1 hour by each pump. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A large pump can fill a 10,000 gallon tank 5 hours faster than a small pump.
The large pump outputs water 100 gallons per hour faster than the small pump.
Find the number of gallons pumped in 1 hour by each pump.
:
Let x = gal/hr of the smaller pump
(x+100) = gal/hr of the larger pump
:
small pump time - large pump time = 5 hrs - = 5
multiply by x(x+100), results
10000(x+100) - 10000x = 5x(x+100)
:
10000x + 1000000 - 10000x = 5x^2 + 500x
A quadratic equation
0 = 5x^2 + 500x - 1000000
Simplify, divide by 5
x^2 + 100x - 200000 = 0
Factors
(x + 500)(x - 400) = 0
x = 400 gal/hr, the rate of the small pump
and
400 + 100 = 500 gal/hr, the rate of the large pump
:
:
Check solution, find the time of each pump
10000/400 = 25 hrs
10000/500 = 20 hrs
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difference: 5 hrs
