document.write( "Question 655409: Henry and Irene working together can wash all the windows of their house in 5 h 40 min. Working alone, it takes Henry 8 1/2h more than Irene to do the job. How long does it take each person working alone to wash all the windows? \n" ); document.write( "

Algebra.Com's Answer #409126 by Edwin McCravy(20055) $\"\"$ $\"About$

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Henry and Irene working together can wash all the windows of their house in 5 h 40 min. Working alone, it takes Henry 8 1/2h more than Irene to do the job. How long does it take each person working alone to wash all the windows?
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document.write( "Make this chart:\r\n" );
document.write( "                                |no. of jobs | no of hours| Rate in  |\r\n" );
document.write( "                                |   done     |  required  | jobs/hour|  \r\n" );
document.write( "---------------------------------------------------------------------|\r\n" );
document.write( "Henry washing alone             |            |            |          |\r\n" );
document.write( "Irene washing alone             |            |            |          |\r\n" );
document.write( "Henry and Irene washing together|            |            |          |\r\n" );
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document.write( "Let's let x = the number of hours required for Irene to do 1 job.\r\n" );
document.write( "Then it takes Henry x+8.5 to do 1 job.  We are told that working \r\n" );
document.write( "together they can finish 1 job in 5 hours 40 minutes or \r\n" );
document.write( "or  hours.  \r\n" );
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document.write( "So we fill in those times and 1's for the number of jobs done in each \r\n" );
document.write( "of the three cases.  [In other problemsn they may do 2 jobs or 3 jobs \r\n" );
document.write( "or more, but in this problem they just do 1 job:  \r\n" );
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document.write( "                                |no. of jobs | no of hours| Rate in  |\r\n" );
document.write( "                                |   done     |  required  | jobs/hour|  \r\n" );
document.write( "---------------------------------------------------------------------|\r\n" );
document.write( "Henry washing alone             |     1      |  x+8.5     |          |\r\n" );
document.write( "Irene washing alone             |     1      |    x       |          |\r\n" );
document.write( "Henry and Irene washing together|     1      |   17/3     |          |\r\n" );
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document.write( "Next we fill in the rate in jobs/hour by dividing jobs by hours:\r\n" );
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document.write( "                                |no. of jobs | no of hours| Rate in  |\r\n" );
document.write( "                                |   done     |  required  | jobs/hour|  \r\n" );
document.write( "---------------------------------------------------------------------|\r\n" );
document.write( "Henry washing alone             |     1      |  x+8.5     | 1/(x+8.5)|\r\n" );
document.write( "Irene washing alone             |     1      |    x       |    1/x   |\r\n" );
document.write( "Henry and Irene washing together|     1      |   17/3     |   3/17   |\r\n" );
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document.write( "             The equation comes from:\r\n" );
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document.write( "              +   =  \r\n" );
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document.write( "              +  = \r\n" );
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document.write( "Solve that and get 8.5 hours for Irene and  or 5 hours 40 minutes for Henry.\r\n" );
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document.write( "Edwin

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