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

Algebra ->  Rate-of-work-word-problems -> 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       Log On


   

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) About Me  (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)
t%2F8 + t%2F5 = 1
Multiply by 40 to clear the denominators, results:
5t + 8t = 40
13t = 40
t = 40%2F13
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
t%2F8 + %28%286-t%29%29%2F5 = 1
multiply by 40 again, results:
5t + 8(6-t) = 40
5t + 48 - 8t = 40
5t - 8t = 40 - 48
-3t = -8
t = %28-8%29%2F%28-3%29
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)