SOLUTION: working together two servicemen can clean a swimming pool in 6 hours. If both of them worked together for the first three hours, and the first stopped for one reason or another, it

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Question 919064: working together two servicemen can clean a swimming pool in 6 hours. If both of them worked together for the first three hours, and the first stopped for one reason or another, it will require the second 4 hours more to rub clean the pool. How long does it take each of them separately to do the job?
Found 2 solutions by josgarithmetic, lwsshak3:
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Rates as jobs per hour:
First, 1%2Fx
Second, 1%2Fy.
Both together, highlight_green%281%2Fx%2B1%2Fy=1%2F6%29

The details of the job being done yield, according RT=J rate time job,
highlight_green%28%281%2Fx%2B1%2Fy%293%2B%281%2Fy%294=1%29;

The green-outlined equations are the system to solve for x and y. Algebraic arithmetic steps needed to solve the system.

A substitution can be made to begin.
The second equation becomes, using substitution,
%281%2F6%293%2B%281%2Fy%294=1, containing just one single unknown variable.

The other tutor already provided complete arithmetic steps; only that variable assignments were switched compared to mine.

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
working together two servicemen can clean a swimming pool in 6 hours. If both of them worked together for the first three hours, and the first stopped for one reason or another, it will require the second 4 hours more to rub clean the pool. How long does it take each of them separately to do the job?
***
let x=amt of time 2nd can finish the separately
1/x=his work rate
let y=amt of time 1st can finish the separately
1/y=his work rate
6 hrs=amt of time 1st and 2nd working together can finish the job
1/6=their work rate
..
3*(1/6)+4*(1/x)=1 (100% completion of job)
3/6+4/x=1
4/x=1-3/6=1/2
x=8
..
working together:
1/y+1/x=1/6
1/y=1/6-1/x
1/y=1/6-1/8=4/24-3/24=1/24
y=24
..
amt of time 2nd can finish the job separately=8 hrs
amt of time 1st can finish the job separately=24 hrs