Question 1001707
The question is:
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how long would each take to do the job alone?
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Let x = the number of days it takes for A to do 1 job.

Then A's rate in jobs per day is 1 job per x days or 1/x jobs per day.

Let y = the number of days it takes for B to do 1 job.

Then B's rate in jobs per day is 1 job per y days or 1/y jobs per day.
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A and B together can finish a job in 36 days.
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Then their combined rate is 1 job per 36 days, or 1/36 jobs per day.

The sum of their rates equals 1/36 jobs per day.

1/x + 1/y = 1/36
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If A can do as much work in 4 days as B can do in 9 days, 
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We use rate×time to determine what part of a job is done by A
in 4 days and what part of a job is done by B in 9 days, and
set those equal to each other:

4/x = 9/y

or

4/x - 9/y = 0

The system of equations is

{{{system(matrix(2,5,1/x,""+"",1/y,""="",1/36,
                     4/x,""-"",9/y,""="",0) )}}}

Do not clear of fractions. Instead eliminate 1/y
by multiplying the first equation through by 9

{{{system(matrix(2,5,9/x,""+"",9/y,""="",1/4,
                     4/x,""-"",9/y,""="",0) )}}}

Adding the two equations:

{{{matrix(1,3,13/x,""="",1/4)}}}

cross multiply 

x = 52 days = how many days it takes for A to do the job.

Substitute in

{{{matrix(1,3,4/x,""="",9/y)}}}

{{{matrix(1,3,4/52,""="",9/y)}}}

{{{matrix(1,3,1/13,""="",9/y)}}}

Cross multiply

y = 117 days = how many days it takes for B to do the job.

Edwin</pre>