SOLUTION: Jim cleans the house in 8 hours. Adam and Jim together clean the house in 5 hours. How long does it take Adam to clean the house by himself?

Click here to see ALL problems on Rate-of-work-word-problems

Question 516758: Jim cleans the house in 8 hours. Adam and Jim together clean the house in 5 hours. How long does it take Adam to clean the house by himself?
Found 2 solutions by mananth, oberobic:
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
Jim ---------- 8 hours
so he does 1/8 of job in 1 hour
together they take 5 hours
so they do 1/5 of job in 1 hour
1/5 -1/8 = 3/40
Adam alone does 3/40 of the job in 1 hour
so he tales 40/3 hours to do it alone
40/3 =13.33 hours

Answer by oberobic(2304) (Show Source):
You can put this solution on YOUR website!
These problems involve determining the fraction of work each resource does per unit of time.
Jim cleans the house in 8 hr, so he does 1/8 of the job per hr.
Adam and Jim clean the house in 5 hr, so their combined work is 1/5 of job per hr.
What is missing is Adam's rate of work, which we will define as 1/a of the job per hr.
.
(1/8 + 1/a) * 5 hr = 1 whole job
.
1/8 + 1/a = 1/5
1/a = 1/5 - 1/8
1/a = 8/40 - 5/40
1/a = 3/40
.
So Adam can do 3/40 of the job per hr.
.
Check to see if they can do the job in 5 hr working together.
.
(1/8 + 3/40)*5 = ?
.
(5/40 + 3/40)*5 = (8/40)*5 = 40/40 = 1 whole job in 5 hr
.
How long does it take Adam to do the job working alone?
.
3/40 *x = 1
.
x = 40/3 = 13 1/3 hr
.
Done.