SOLUTION: A and B together can finish a job in 36 days. If A can do as much work in 4 days as B can do in 9 days, how long would each take to do the job alone?

Question 1001707: A and B together can finish a job in 36 days. If A can do as much
work in 4 days as B can do in 9 days, how long would each take to
do the job alone?
Answer by Edwin McCravy(20059) (Show Source): You can put this solution on YOUR website!
The question is:

how long would each take to do the job alone?

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.

A and B together can finish a job in 36 days.

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

If A can do as much work in 4 days as B can do in 9 days,

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



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



Adding the two equations:



cross multiply 

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

Substitute in







Cross multiply

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

Edwin

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