1. ## SAT Work Problem

I can't seem to figure out the following problem and how to set it up:

Paul and Mary can do a job in 2 hours. When Paul works alone, he can do 5 jobs in 15 hours. How many jobs can Mary do in 12 hour, alone?

The answer in the SAT book says 2 jobs.

Thanks.

2. Originally Posted by Tracer
I can't seem to figure out the following problem and how to set it up:

Paul and Mary can do a job in 2 hours. When Paul works alone, he can do 5 jobs in 15 hours. How many jobs can Mary do in 12 hour, alone?

The answer in the SAT book says 2 jobs.

Thanks.
It might help if you write units everwhere, and the units will tell you what needs to be multiplied with what

let P = Paul's rate, which will be jobs/hour
let M = Mary's rate, which will be jobs/hour

So P+M = 1/2 jobs/hour

P = 5/15 = 1/3 jobs/hour

So M = 1/2 - 1/3 = 1/6 jobs/hour

So in 12 hours, Mary can do 2 jobs. (If you want to write explicitly, multiply 12 hours by 1/6 jobs/hour).

3. Hello, Tracer!

Paul and Mary can do a job in 2 hours.
When Paul works alone, he can do 5 jobs in 15 hours.
How many jobs can Mary do in 12 hour, alone?

We are told: Paul can do 5 jobs in 15 hours.
. . Hence, he can do 1 job in 3 hours.
In one hour, Paul can do $\frac{1}{3}$ of a job.

Let $M$ = number of hours for Mary to do a job alone.
In one hour, she can do $\frac{1}{M}$ of the job.

Working together for one hour, they can do: . $\frac{1}{3} + \frac{1}{M}$ of the job. .[1]

Working together, they can do the job in 2 hours.
Working together for one hour, they can do $\frac{1}{2}$ of the job. .[2]

Note that [1] and [2] both describe the same quantity.

There is our equation! . . . . $\dfrac{1}{3} + \dfrac{1}{M} \:=\:\dfrac{1}{2}$

Multiply by $6M\!:\;\;2M + 6 \:=\:3M \quad\Rightarrow\quad M \:=\:6$

Hence. Mary takes 6 hours to do a job alone.

Therefore, in 12 hours she can do 2 jobs.

Edit: I was too slow again . . .
. . . .This is a slight variation of undefined's solution.
.