SOLUTION: A and B working together can complete a job in 30 days. After they had both worked 18 days, however, A left and B finished the work in 20 more days. Find the time in which each can

Question 1121174: A and B working together can complete a job in 30 days. After they had both worked 18 days, however, A left and B finished the work in 20 more days. Find the time in which each can do the work alone.
Found 2 solutions by ankor@dixie-net.com, ikleyn:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A and B working together can complete a job in 30 days.
After they had both worked 18 days, however, A left and B finished the work in 20 more days.
Find the time in which each can do the work alone.
:
let a = time A required to complete the job alone
let b = time for B alone
let the completed job = 1
:
Write an equation for each statement
"A and B working together can complete a job in 30 days."
+ = 1
multiply eq by ab
30b + 30a = ab
"After they had both worked 18 days, however, A left and B finished the work in 20 more days."
+ = 1
18b + 38a = ab
:
ab = ab therfore
18b + 38a = 30b + 30a
38a - 30a = 30b - 18b
8a = 12b
a = b
a = 1.5b
:
Using the first equation, replace a with 1.5b
+ = 1
multiply by b
+ 30 = b
20 + 30 = b
b = 50 hrs B working alone
then find a
1.5(50) = 75 hrs b working alone

Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
.

After A and B worked 18 days together, they made = of the job; so, of the job remained. Then B completed this of the job in 20 days - so, his rate of work is = = of the job per day. Thus they both have the combined rate of work of the job per day working together, and the B's individual rate of work is . Hence, the A's rate of work is - = - = = . Answer. A can do the job in 75 days working alone. B can do the job in 50 days working alone.

Solved.

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