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?

Algebra ->  Rate-of-work-word-problems -> 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?      Log On


   

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(20056) About Me  (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:

matrix%281%2C3%2C13%2Fx%2C%22%22=%22%22%2C1%2F4%29

cross multiply 

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

Substitute in

matrix%281%2C3%2C4%2Fx%2C%22%22=%22%22%2C9%2Fy%29

matrix%281%2C3%2C4%2F52%2C%22%22=%22%22%2C9%2Fy%29

matrix%281%2C3%2C1%2F13%2C%22%22=%22%22%2C9%2Fy%29

Cross multiply

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

Edwin