SOLUTION: A bathtub which can hold 46.5 gallons has a leaky stopper. The maximum rate that the water flow a from the tap into the tub is 17 gallons/minute. If the tub is initially empty and

Question 1134961: A bathtub which can hold 46.5 gallons has a leaky stopper. The maximum rate that the water flow a from the tap into the tub is 17 gallons/minute. If the tub is initially empty and the tap is turned on to its maximum flow, the tub fills in 3 minutes. If the full tub were left to sit, it would take how long (in minutes) to drain through the leaky stopper?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

It takes 3 minutes, at 17 gallons per minute, for the tap to fill the tub, so 51 gallons of water flow into the tub.

The capacity of the tub is 46.5 gallons; so in 3 minutes 51-46.5 = 4.5 gallons have leaked. That's a rate of 4.5/3 = 1.5 gallons per minute.

The amount of time it will take the tub to drain at that rate is 46.5/1.5 = 31 minutes.
Answer by ikleyn(52796)   (Show Source): You can put this solution on YOUR website!
.

The problem in the post is formulated incorrectly.

Its formulation misses two different conception:   a) "bathtub leaky stopper"   and   b) "drainage pipe".

For a bathtub, a drainage pipe is able to drain water all the time, while water does present in the bathtub.

A "bathtub leaky stopper" works removing water from the bathtub only when the water level in the bathtub
achieves or is above a certain level.

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If to formulate the problem correctly, it becomes a standard joint work problem, to which tons of solutions
and a methodology are presented in lessons
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive
in this site.

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