SOLUTION: A pool has an inlet pipe to fill it and an outlet pipe to empty it. It takes 2 hours longer to empty the pool than it does it fill it. The inlet pipe is turned on to fill the pool,

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A pool has an inlet pipe to fill it and an outlet pipe to empty it. It takes 2 hours longer to empty the pool than it does it fill it. The inlet pipe is turned on to fill the pool,      Log On


   

Question 436582: A pool has an inlet pipe to fill it and an outlet pipe to empty it. It takes 2 hours longer to empty the pool than it does it fill it. The inlet pipe is turned on to fill the pool, but the outlet pipe is accidentally open. Despite this, the pool fills in 8 hours. How long does it take the outlet pipe to empty the pool? Round to the nearest tenth.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A pool has an inlet pipe to fill it and an outlet pipe to empty it.
It takes 2 hours longer to empty the pool than it does it fill it.
The inlet pipe is turned on to fill the pool, but the outlet pipe is accidentally open.
Despite this, the pool fills in 8 hours.
How long does it take the outlet pipe to empty the pool? Round to the nearest tenth.
:
Let t = time required to fill the pool (+)
then
(t+2) = time required to empty the pool (-)
:
Let the completed job = 1; (a full pool)
:
8%2Ft - 8%2F%28%28t%2B2%29%29 = 1
Multiply by t(t+2), results:
8(t+2) - 8t = t(t+2)
8t + 16 - 8t = t^2 + 2t
A quadratic equation
t^2 + 2t - 16 = 0
Use the quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this problem; x=t; a=1; b=2; c=-16
t+=+%28-2+%2B-+sqrt%282%5E2-4%2A1%2A-16+%29%29%2F%282%2A1%29+
:
t+=+%28-2+%2B-+sqrt%284+-+%28-64%29+%29%29%2F2+
t+=+%28-2+%2B-+sqrt%284+%2B+64+%29%29%2F2+
t+=+%28-2+%2B-+sqrt%2868+%29%29%2F2+
Two solutions, but only care about the positive one,
t+=+%28-2+%2B+8.246%29%2F2+
t = 6.246%2F2
t = 3.123
then
3.123 + 2 = 5.123 ~ 5.1 hrs to empty the pool
:
:
Check this
8/3.123 - 8/5.123 = 1.00; confirms our solution