SOLUTION: An old pump takes 6 hours longer to empty a pool than does a new pump. With both pumps working, the pool can be emptied in 4 hours. Find the time for the new pump working along t
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Question 595340: An old pump takes 6 hours longer to empty a pool than does a new pump. With both pumps working, the pool can be emptied in 4 hours. Find the time for the new pump working along to empty the tank
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
An old pump takes 6 hours longer to empty a pool than does a new pump.
With both pumps working, the pool can be emptied in 4 hours.
Find the time for the new pump working alone to empty the tank
:
let n = time for the new pump to empty the pool
then
(n+6) = time for the old pump to do it
:
Let the completed job = 1, (an empty pool)
:
+ = 1
:
Multiply by n(n+6)
n(n+6)* + n(n+6)* = n(n+6)
Cancel out the denominators
4(n+6) + 4n = n^2 + 6n
4n + 24 + 4n = n^2 + 6n
8n + 24 = n^2 + 6n
Combine like terms on the right
0 = n^2 + 6n - 8n - 24
n^2 - 2n - 24 = 0
Factors to
(n-6)(n+4) = 0
the positive solution
n = 6 hrs time for the new pump alone
:
:
See if that checks out
+ =
+ = 1
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