SOLUTION: A water faucet can fill a sink in 15 minutes, whereas the drain can empty it in 6 minutes. If the sink is full, how long will it take to empty if both the faucet and the drain ar

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Question 1055872: A water faucet can fill a sink in 15 minutes, whereas the drain can empty it in 6 minutes.
If the sink is full, how long will it take to empty if both the faucet and the drain are open?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Another constant rates situation much as if doing a job, doing a quantity of work.

RT=V, here, volume unit is just for 1 SINK.

%281%2F15%29t-%281%2F6%29t=-1
The negative 1 for the amount of volume is because I have taken FILLING to be POSITIVE, and EMPTYING to be NEGATIVE.

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
A water faucet can fill a sink in 15 minutes, whereas the drain can empty it in 6 minutes. If the sink is full, how long will it take to empty if both the faucet and the drain are open?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

1%2F6+-+1%2F15 = 15%2F90+-+6%2F90 = 9%2F90 = 1%2F10 of the tank volume goes out every minute.

Answer. The tank will be emptied in 10 minutes.

Solved.


For a wide variety of similar solved joint-work problems with detailed explanations see the 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.

Read them and get be trained in solving joint-work problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
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The referred lessons are the part of this textbook under the topic "Rate of work and joint work problems" of the section "Word problems".