SOLUTION: A small pump can drain a pool in 8 hours. A large pump can drain it in 5 hrs.
How long will it take them to drain the pool simultaneously? Suppose that the pumps could not be
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Question 396793: A small pump can drain a pool in 8 hours. A large pump can drain it in 5 hrs.
How long will it take them to drain the pool simultaneously? Suppose that the pumps could not be used simultaneously and that the pool was drained in exactly 6 hours. How long was each pump used?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A small pump can drain a pool in 8 hours.
A large pump can drain it in 5 hrs.
How long will it take them to drain the pool simultaneously?
:
Let t = time required when both pumps are used
Let the completed job = 1; (a drained pool)
+ = 1
Multiply by 40 to clear the denominators, results:
5t + 8t = 40
13t = 40
t =
t = 3.077 hrs or about 3 hrs 4.6 min
:
Suppose that the pumps could not be used simultaneously and that the pool was drained in exactly 6 hours. How long was each pump used?
:
Let t = operating time of the small pump
then
(6-t) = operating time of the large pump
+ = 1
multiply by 40 again, results:
5t + 8(6-t) = 40
5t + 48 - 8t = 40
5t - 8t = 40 - 48
-3t = -8
t =
t = 2.67 hrs time of the small pump (about 2 hrs 40 min)
and
6 - 2.67 = 3.33 hrs time of the large pump (about 2 hrs 20 min)
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