SOLUTION: It takes Pump A 10 minutes longer to fill a tank with water than it takes pump B to fill the same tank. Together the two pumps can fill the tank in 12 minutes. How long does it tak

Question 789823: It takes Pump A 10 minutes longer to fill a tank with water than it takes pump B to fill the same tank. Together the two pumps can fill the tank in 12 minutes. How long does it take each pump to fill the tank alone? I need help setting up the problem. Thank You!
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
t takes Pump A 10 minutes longer to fill a tank with water than it takes pump B to fill the same tank. Together the two pumps can fill the tank in 12 minutes. How long does it take each pump to fill the tank alone? I need help setting up the problem.
***
let x= minutes pump B takes to fill the tank alone
its work rate=1/x
x+10=minutes pump A takes to fill the tank alone
its work rate=1/(x+10)
12=minutes it takes to fill the tank pumps A & B working together
1/12=Their work rate
sum of individual work rates=work rate working together.
(1/x)+(1/(x+10))=1/12
x+10+x=(x^2+10x)/12
24x+120=x^2+10x
x^2-14x-120=0
(x+6)(x-20)=0
x=-6(reject)
or
x=20
ans:
minutes pump B takes to fill the tank alone=20
minutes pump A takes to fill the tank alone=x+10=30

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