SOLUTION: Emma can do a job in 12 days. After she has work for 4 days, she is joined by marie. They finish the job together in 2 more days. How long would it take Marie to do the whole job

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Emma can do a job in 12 days. After she has work for 4 days, she is joined by marie. They finish the job together in 2 more days. How long would it take Marie to do the whole job       Log On


   

Question 715924: Emma can do a job in 12 days. After she has work for 4 days, she is joined by marie. They finish the job together in 2 more days. How long would it take Marie to do the whole job alone?
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
A good way to handle work-rate job completion is to use Rate*Time=Jobs, with the rate being expressed as how many jobs per unit time.
Let e = Emma's rate = 1/12 jobs per day
Let m = marie's rate, unknown

Progress of the job: highlight%28%281%2F12%29%2A4%2B%281%2F12%2Bm%29%2A2=1%29
Examine the equation to see that for two days working together, Marie's and Emma's rates are combined by addition.

The task now is to calculate m from that equation, m being Marie's rate alone.

%281%2F12%2Bm%29%2A2=1-%284%2F12%29
1%2F6%2B2m=1-1%2F3
2m=1-1%2F3-1%2F6
2m=%286-2-1%29%2F6
2m=1%2F2
highlight%28m=%281%2F4%29%29, JOBS/DAY, according to the way the rate variable was assigned.

That equivalently means, Marie can do this 1 job in 4 days.