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?
<pre>

Make this chart:
                                |no. of jobs | no of hours| Rate in  |
                                |   done     |  required  | jobs/hour|  
---------------------------------------------------------------------|
Henry washing alone             |            |            |          |
Irene washing alone             |            |            |          |
Henry and Irene washing together|            |            |          |


Let's let x = the number of hours required for Irene to do 1 job.
Then it takes Henry x+8.5 to do 1 job.  We are told that working 
together they can finish 1 job in 5 hours 40 minutes or {{{5&2/3}}}
or {{{17/3}}} hours.  

So we fill in those times and 1's for the number of jobs done in each 
of the three cases.  [In other problemsn they may do 2 jobs or 3 jobs 
or more, but in this problem they just do 1 job:  

                                |no. of jobs | no of hours| Rate in  |
                                |   done     |  required  | jobs/hour|  
---------------------------------------------------------------------|
Henry washing alone             |     1      |  x+8.5     |          |
Irene washing alone             |     1      |    x       |          |
Henry and Irene washing together|     1      |   17/3     |          |

Next we fill in the rate in jobs/hour by dividing jobs by hours:

                                |no. of jobs | no of hours| Rate in  |
                                |   done     |  required  | jobs/hour|  
---------------------------------------------------------------------|
Henry washing alone             |     1      |  x+8.5     | 1/(x+8.5)|
Irene washing alone             |     1      |    x       |    1/x   |
Henry and Irene washing together|     1      |   17/3     |   3/17   |


             The equation comes from:

             {{{(matrix(4,1,

"Henry's", rate, in, "jobs/hour"))}}} + {{{(matrix(4,1,

"Irene's", rate, in, "jobs/hour"))}}}  = {{{(matrix(6,1,

Their, rate, working, together, in, "jobs/hour"))}}} 

             {{{1/(x+8.6)}}} + {{{1/x}}} = {{{3/17}}}

Solve that and get 8.5 hours for Irene and {{{17/3}}} or 5 hours 40 minutes for Henry.

Edwin</pre>