SOLUTION: Jane takes 4 hours to do a job that Alice can do in 3 hours. If Jane works 1/2 hour before Alice joins her, how long will it take the two of them to finish the job?

Question 587005: Jane takes 4 hours to do a job that Alice can do in 3 hours. If Jane works 1/2 hour before Alice joins her, how long will it take the two of them to finish the job?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Jane takes 4 hours to do a job that Alice can do in 3 hours.
If Jane works 1/2 hour before Alice joins her, how long will it take the two of them to finish the job?
:
Let t = time required to finish the job together
then
(t+.5) = total time worked by Jane
:
Let the completed job = 1
:
Each girl will do a fraction of the job, the two fractions add up to 1
+ = 1
multiply by 12
12* + 12* = 12
Cancel the denominators
4t + 3(t+.5) = 12
3t + 4t + 1.5 = 12
7t = 12 - 1.5
7t = 10.5
t =
t = 1.5 hrs to finish the job together
:
:
Check (J works 2 hrs)
+ = 1
.5 + .5 = 1
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