SOLUTION: Jonathan and Jose could build a shed, working together, in 6 2/3 hours; but Jonathan worked alone for 3 hours and was then joined by Jose, after which they finished the shed in 5 h

Question 407255: Jonathan and Jose could build a shed, working together, in 6 2/3 hours; but Jonathan worked alone for 3 hours and was then joined by Jose, after which they finished the shed in 5 hours. If they were paid according to the amount of work each accomplished, how should $96 be divided between them?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Jonathan and Jose could build a shed, working together, in 6 2/3 hours; but Jonathan worked alone for 3 hours and was then joined by Jose, after which they finished the shed in 5 hours. If they were paid according to the amount of work each accomplished, how should $96 be divided between them?
..
let x=hours Jonathan could finish the job alone
then 1/x = Jonathan's hourly work rate
Working together they can complete the job in 6 2/3 hours or 20/3 hours
Working together hourly work rate =1/(20/3)=3/20
Let 1/y = Jose's hourly work rate
sum of individual work rates = work rate working together
1/x + 1/y = 3/20
1/y = 3/20 - 1/x
Jonathan worked for 8 hours
Jose worked for 5 hours
To complete the job,
Jonathan's contribution=8*(1/x)
Jose's contribution=5*(3/20 - 1/x)
8*(1/x)+5*(3/20 - 1/x)=1
8/x+15/20-5/x=1
3/x=1-15/20=1/4
x=12
Jonathan's contribution to the job=8*(1/12)=2/3
Jose's contribution to the job=5*(3/20-1/12)=5(9/60-5/60)=5*(4/60)=1/3
Ans:
Jonathan should be paid $64 for the amount of work he did.
Jose should be paid $32 for the amount of work he did.

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