SOLUTION: A bath tub can be filled by the cold water and hot water pipes in 10 mins and 15 mins, respectively. A person leaves the bathroom after turning on both pipes simultaneously and ret

Question 767278: A bath tub can be filled by the cold water and hot water pipes in 10 mins and 15 mins, respectively. A person leaves the bathroom after turning on both pipes simultaneously and returns at the moment when the bath should be full. Finding, however, that the waste pipe has been open, he then closes it. In exactly 4 mins more the bath is fill. In how much time would the waste pipe empty the full bath, if it alone is opened.
Answer by josgarithmetic(39623) (Show Source): You can put this solution on YOUR website!
Look at the cold & hot combined rate.
In units of tub per minute, you have tub per minute, not here showing that arithmetic process. The EXPECTED length of time to fill the tub was 6 minutes, so this person let the faucets fill for 6 minutes.

BUT the drain was also open, its rate an unknown, r.

Let us use where R is rate in tubs or vessel-fulls per minute, m is minutes, and v is vessel-fulls, in this case, meaning tubs. Also think clearly about the variables. R is for "in general" and r is for our specific tub's drain pipe. Also be aware, . r is negative.

So we have two parts of the job. One part when all three drains were open for 6 minutes:
-
and the part when our person closed the drain pipe and the tub continued to fill for 4 minutes:

The sum of those two expressions is the quantity of 1 tub.

SOLVE FOR r. That is the rate of draining the tub for the drain pipe.
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