SOLUTION: Two pumps can fill a water tank in 45 minutes when working together. Alone, the second pump takes 3 times longer than the first to fill the tank. How long does it take the first pu

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Two pumps can fill a water tank in 45 minutes when working together. Alone, the second pump takes 3 times longer than the first to fill the tank. How long does it take the first pu      Log On


   

Question 189389: Two pumps can fill a water tank in 45 minutes when working together. Alone, the second pump takes 3 times longer than the first to fill the tank. How long does it take the first pump alone to fill the tank
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two pumps can fill a water tank in 45 minutes when working together.
Alone, the second pump takes 3 times longer than the first to fill the tank.
How long does it take the first pump alone to fill the tank?
:
Let x = time required for the first pump to fill the tank alone
then
3x = time required for the 2nd pump to do it alone
:
Write an equation of them working together; let the full tank = 1
Each pump will do a fraction of the job and will equal 1 when added together
:
45%2Fx + 45%2F%283x%29 = 1
Multiply equation by 3x, results
3(45) + 45 = 3x
:
135 + 45 = 3x
:
180 = 3x
x = 180%2F3
x = 60 min for pump 1 alone
:
;
Check solution; (2nd pump requires 3*60 = 180 min alone)
45%2F60 + 45%2F180 =
.75 + .25 = 1; confirms our solution