document.write( "Question 1208808: A tub can be filled with hot water in 18 minutes, or with cold water in 12 minutes. The tub can also be emptied when the plug is pulled out, in 9 minutes. Farley ran the hot water in his tub for 8 minutes, then both the cold and hot water together for 2 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?
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document.write( "A tub can be filled with hot water in 18 minutes, or with cold water in 12 minutes. The tub can also be emptied when the plug is pulled out, in 9 minutes. Farley ran the hot water in his tub for 8 minutes, then both the cold and hot water together for 2 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?\r\n" );
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document.write( "Time tub can be filled with hot water: 18 minutes, which means that \"1%2F18\" of tub can be filled with hot water in 1 minute\r\n" );
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document.write( "Time tub can be filled with cold water: 12 minutes, which means that \"1%2F12\" of tub can be filled with cold water in 1 minute\r\n" );
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document.write( "With hot water being run for 8 minutes, and both hot and cold water for 2 minutes, fraction of tub thatw's filled with hot\r\n" );
document.write( "and cold water in those 10 minutes = \r\n" );
document.write( "                                           \"matrix%281%2C5%2C+20%2F36+%2B+6%2F36%2C+%22=%22%2C+26%2F36%2C+%22=%22%2C+13%2F18%29\"\r\n" );
document.write( "\"13%2F18\" of tub was filled in the 8 minutes that the hot water ran for, alone, and the 2 minutes thereafter that both hot and cold ran, together\r\n" );
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document.write( "Therefore, \"matrix%281%2C3%2C+1+-+13%2F18%2C+%22=%22%2C+5%2F18%29\" of tub was left to be filled\r\n" );
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document.write( "Time tub can be emptied after plug is pulled: 9 minutes, which means that \"1%2F9\" of tub can be EMPTIED in 1 minute\r\n" );
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document.write( "Now, with the plug being pulled, and fill-time being T, we get: \r\n" );
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document.write( "Cross-multiplying, we get the TIME taken to fill the tub, after the plug was pulled, or T = 10 minutes.
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