SOLUTION: A tub can be filled with hot water in 15 minutes, or with cold water in 12 minutes. The tub can also be emptied when the plug is pulled out, in 10 minutes. Farley ran the hot water

Question 1147570: A tub can be filled with hot water in 15 minutes, or with cold water in 12 minutes. The tub can also be emptied when the plug is pulled out, in 10 minutes. Farley ran the hot water in his tub for 6 minutes, then both the cold and hot water together for 3 minutes, and then with the two taps still running, he accidentally pulled the plug. How long, did it take in minutes, for the tub to fill after the plug was pulled?
Found 2 solutions by VFBundy, josgarithmetic:
Answer by VFBundy(438) (Show Source): You can put this solution on YOUR website!
Rate hot water fills tub = 1/15 tub per minute
Rate cold water fills tub = 1/12 tub per minute
Rate tub is "filled" when plug is pulled = -1/10 tub per minute

Rate hot and cold water together fills tub = 1/15 + 1/12 = 3/20 tub per minute

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Farley ran the hot water in his tub for 6 minutes

Rate * Time = Portion of job completed

1/15 * 6 = 6/15 = 2/5

We start with the whole tub needing to be filled. After this step was completed, 2/5 of the tub was filled, meaning 3/5 of the tub still needs to be filled.

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Then both the cold and hot water together for 3 minutes

Rate * Time = Portion of job completed

3/20 * 3 = 9/20

Before this step, 3/5 of the tub needed to be filled. This step filled 9/20 of the tub. So, after this step, "3/5 minus 9/20" of the tub still needs to be filled...or, 3/20 tub still needs to be filled.

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Then with the two taps still running, he accidentally pulled the plug.

So, we have the two taps running (rate of 3/20 of tub per minute) AND we also have the plug pulled (rate of -1/10 of the tub per minute.) So, together, the rate is: 3/20 - 1/10...or, 1/20 of the tub per minute.

We need to find how long it takes to fill the tub from this point. Remember from the previous step, that 3/20 of the tub remained to be filled.

Using the formula:

Rate * Time = Portion of job completed

1/20 * Time = 3/20

Time = 3

So, the answer is 3 minutes.
Answer by josgarithmetic(39613) (Show Source): You can put this solution on YOUR website!
ONE tub

6 minutes hot water in:

3 minutes hot and cold water in:

x minutes hot, cold, and opened drain plug:

Simplify and solve for x.
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