SOLUTION: with both hot and cold water running, a bathtub can be filled in 10 minutes. The drain will empty the tub in 15 minutes. A child turns both faucets on and leaves the drain open.

Algebra ->  Rate-of-work-word-problems -> SOLUTION: with both hot and cold water running, a bathtub can be filled in 10 minutes. The drain will empty the tub in 15 minutes. A child turns both faucets on and leaves the drain open.       Log On


   



Question 547604: with both hot and cold water running, a bathtub can be filled in 10 minutes. The drain will empty the tub in 15 minutes. A child turns both faucets on and leaves the drain open. How long will it be before the bathtub starts to overflow?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Sum up the rates of filling and draining
to get the rate with both faucets open
and drain open
--------------
( 1 tub ) / ( 10 min ) = rate of filling with
both faucets open
( 1 tub ) / (15 min ) = rate of emptying
with drain open
--------------
Let +t+ = time to fill tub in min
+1%2F10+-+1%2F15+=+1%2Ft+
Multiply both sides by +30t+
+3t+-+2t+=+30+
+t+=+30+
In 30 min the tub will start to overflow