SOLUTION: Jim and Shirley, working together, can rake the yard in 3 hours. Working alone, Shirley takes three times as long as Jim. How long does it take Jim to rake the yard alone?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Jim and Shirley, working together, can rake the yard in 3 hours. Working alone, Shirley takes three times as long as Jim. How long does it take Jim to rake the yard alone?      Log On


   

Question 996414: Jim and Shirley, working together, can rake the yard in 3 hours. Working alone, Shirley takes three times as long as Jim. How long does it take Jim to rake the yard alone?
Found 2 solutions by lwsshak3, josgarithmetic:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Jim and Shirley, working together, can rake the yard in 3 hours. Working alone, Shirley takes three times as long as Jim. How long does it take Jim to rake the yard alone?
let x=time it takes jim to rake the yard alone
1/x=his work rate
let x=time it takes Shirley to rake the yard alone
1/3x=her work rate
sum of indv. work rates=work rate working together
1/x+1/3x=1/3
lcd:3x
3+1=x
x=4
time it takes jim to rake the yard alone=4 hrs

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
           JIM      SHIRLEY     TOGETHER

RATE        1/t      1/(3t)      1/3


Rate for Jim and Shirley together is the sum of their individual rates.
highlight_green%281%2Ft%2B1%2F%283t%29=1%2F3%29
Solve for t.