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
or 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:
+ =
+ =
Solve that and get 8.5 hours for Irene and or 5 hours 40 minutes for Henry.
Edwin