# 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?

Aug 29, 2017

$\frac{12}{7} \text{hr}$

#### Explanation:

If Janet can do the job in $3$ hours, then in $1$ hour she can do $\frac{1}{3}$ of the job. Similarly, if Tom can do the job in $4$ hours, in $1$ hour he'll do $\frac{1}{4}$ 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

$\frac{1}{3} x + \frac{1}{4} x = 1$

because $\frac{1}{3} x$ is the total time (in hours) that Janet will take, and $\frac{1}{4} x$ 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 $x$.

$\frac{1}{3} x + \frac{1}{4} x = 1$

$\frac{4}{12} x + \frac{3}{12} x = 1$

$\frac{7}{12} x = 1$

$x = \frac{12}{7} \text{hr}$

So, it takes them $\frac{12}{7} \text{hr}$ or about $\text{1.7 hr}$ to complete the job working together.