Question 1147570
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
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Rate hot and cold water together fills tub = 1/15 + 1/12 = 3/20 tub per minute
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<i>Farley ran the hot water in his tub for 6 minutes</i>
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Rate * Time = Portion of job completed
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1/15 * 6 = 6/15 = 2/5
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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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<i>Then both the cold and hot water together for 3 minutes</i>
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Rate * Time = Portion of job completed
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3/20 * 3 = 9/20
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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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<i>Then with the two taps still running, he accidentally pulled the plug.</i>
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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.
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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.
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Using the formula:
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Rate * Time = Portion of job completed
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1/20 * Time = 3/20
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Time = 3
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So, the answer is 3 minutes.