Question

Janet, an experienced shipping clerk, can fill a certain order in 3 hours. Tom, a new clerk, needs 4 hours to do the same job. How long does it take them working together?

Answer 1

`12/7 "hr"`

Explanation:

If Janet can do the job in `3` hours, then in `1` hour she can do `1/3` of the job. Similarly, if Tom can do the job in `4` hours, in `1` hour he'll do `1/4` of the job.

Let's say that the total amount of time they take to do the job working together is `x` hours.

We can then write the equation

`1/3x + 1/4x = 1`

because `1/3x` is the total time (in hours) that Janet will take, and `1/4x` is the total time (in hours) that Tom will take. Since they're working together, we're adding the two times. This is equal to `1` because `1` represents the whole job.

To solve this equation, rewrite the fractions so they have a common denominator, and find `x`.

`1/3x + 1/4x = 1`

`4/12x + 3/12x = 1`

`7/12x = 1`

`x=12/7 "hr"`

So, it takes them `12/7 "hr"` or about `"1.7 hr"` to complete the job working together.