document.write( "Question 1169052: Tom and dick working together can perform a task in 2 hours and 24 minutes. Dick and harry working together can perform the same task in 3 hours and 36 minutes. If dick works alone, he can complete the task in 6 hours. How long will it take tom and harry perform the task working together ? \n" ); document.write( "

Algebra.Com's Answer #793701 by ikleyn(52776) $\"\"$ $\"About$

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\n" ); document.write( "Tom and dick working together can perform a task in 2 hours and 24 minutes.
\n" ); document.write( "Dick and harry working together can perform the same task in 3 hours and 36 minutes.
\n" ); document.write( "If dick works alone, he can complete the task in 6 hours.
\n" ); document.write( "How long will it take tom and harry perform the task working together ?
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document.write( "Let T be the rate of Tom  (i.e. the part of the job he makes in each hour).\r\n" );
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document.write( "Let D be the rate of work for Dick, and\r\n" );
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document.write( "let H be the rate of work for Harry.\r\n" );
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document.write( "Then we have these two equations\r\n" );
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document.write( "    T + D =  =     (1)   (here    represents  2  hours = 2 hours and 24 minutes)\r\n" );
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document.write( "    H + D =  =     (2)   (here    represents  3  hours = 3 hours and 36 minutes)\r\n" );
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document.write( "Adding these equations, you get\r\n" );
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document.write( "   T + H + 2D =  +  =  +  = .    (3)\r\n" );
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document.write( "We also know that the rate of work for Dick is    of the job per hour.\r\n" );
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document.write( "Hence, from (3) we have\r\n" );
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document.write( "    T + H +  = ,  or\r\n" );
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document.write( "    T + H =  -  =  -  = .\r\n" );
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document.write( "It means that Tom and Harry will complete the job in  hours = 2  hours = 2 hours 46 minutes and 9 seconds (rounded).    ANSWER\r\n" );
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