SOLUTION: It takes George 5 hours to rake all the leaves. With Martha's help, together they can rake all the leaves in 2 hours. How long would it take Martha, working alone, to rake all the

Algebra ->  Rate-of-work-word-problems -> SOLUTION: It takes George 5 hours to rake all the leaves. With Martha's help, together they can rake all the leaves in 2 hours. How long would it take Martha, working alone, to rake all the       Log On


   

Question 1077910: It takes George 5 hours to rake all the leaves. With Martha's help, together they can rake all the leaves in 2 hours. How long would it take Martha, working alone, to rake all the leaves?
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52754) About Me  (Show Source):
You can put this solution on YOUR website!
.
The George and Martha combined rate of work is 1%2F2 of the job per hour.

The George's individual rate of work is 1%2F5 of the job per hour.

It implies that Martha's individual rate of work is 1%2F2+-+1%2F5 = 5%2F10-2%2F10 = 3%2F10of the job per hour.


Hence, Martha will complete the job in 10%2F3 hours = 3 hours and 20 minutes.


For a wide variety of similar solved joint-work problems with detailed explanations see the lessons
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive
in this site.

Read them and get be trained in solving joint-work problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Rate of work and joint work problems" of the section "Word problems".




Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Time for Martha alone, m.

1%2F5%2B1%2Fm=1%2F2
-

%28m%2B5%29%2F%285m%29=1%2F2
m%2B5=5m%2F2
2m%2B10=5m
3m=10
m=10%2F3
highlight%28m=3%261%2F3%29

Martha alone rakes the leaves in 3 hours 20 minutes.