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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 miuntes. 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?

 Oct 27, 2019

The hot water can fill 1/15 of the tub in 1 minute.
The cold water can fill 1/12 of the tub in 1 minute.

Running together, they can fill the tub in:
1/15 + 1/12 = 6 2/3 minutes.

[6 x 1/15] + [3 x 1/15] + [3 x 1/12] =.85 of the tub was filled when he pulled the plug. Or:
1 - 0.85 =0.15 of the tub needs to be filled.

The net filling rate, per minute, when both cold and hot water are running together minus emptying rate, per minute, when the plug is pulled = Net filling rate. So:
1/(6/(2/3)) - 1/10 =0.05 - net filling rate per minute.

So, in order for the remaining 15% of the tub to be filled, it will take:0.15 / 0.05 = 3 - minutes for the tub to be filled.

 Oct 27, 2019

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