SOLUTION: 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 ea

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: 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 ea      Log On

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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?
Answer by Edwin McCravy(20054) About Me  (Show Source):
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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?

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%262%2F3
or 17%2F3 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:

             %28matrix%284%2C1%2C%0D%0A%0D%0A%22Henry%27s%22%2C+rate%2C+in%2C+%22jobs%2Fhour%22%29%29 + %28matrix%284%2C1%2C%0D%0A%0D%0A%22Irene%27s%22%2C+rate%2C+in%2C+%22jobs%2Fhour%22%29%29  =  

             1%2F%28x%2B8.6%29 + 1%2Fx = 3%2F17

Solve that and get 8.5 hours for Irene and 17%2F3 or 5 hours 40 minutes for Henry.

Edwin