SOLUTION: A pump can fill a reservoir in 12 days. A second pump, operating independently, can fill the same reservoir in 8 days. How long will it take to fill the reservoir if both pumps ope

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A pump can fill a reservoir in 12 days. A second pump, operating independently, can fill the same reservoir in 8 days. How long will it take to fill the reservoir if both pumps ope      Log On


   

Question 220582: A pump can fill a reservoir in 12 days. A second pump, operating independently, can fill the same reservoir in 8 days. How long will it take to fill the reservoir if both pumps operate simultaneously?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=amount of time required with both pumps operating simultaneously to fill the reservoir
Then both pumps operating simultaneously fills at the rate of 1/x reservoir per day
The first pump fills at the rate of 1/12 reservoir per day
The second pump fills at the rate of 1/8 reservoir per day
So our equation to solve is:
1/12 + 1/8 = 1/x multiply each term by 24x
2x+3x=24
5x=24 divide each side by 5
x=4.8 days---time required with both pumps operating simultaneously
CK
In 4.8 days, the first pump fills (1/12)*4.8 =0.4 of the tank
In 4.8 days the second pump fills (1/8)*4.8=0.6 of the tank
0.4 + 0.6 = 1
1=1 (1 tank, that is)
Hope this helps---ptaylor