# Sue, an experienced shipping clerk, can fill a certain order in 9 hours. Felipe, a new clerk, needs 11 hours to do the same job. Working together, how long will it take them to fill the order?

Jan 9, 2017

$4$ hours and $57$ minutes.

#### Explanation:

Here's one method:

The least common multiple of $9$ and $11$ is $99$.

In $99$ hours, Sue could fill $\frac{99}{9} = 11$ orders, while Felipe could fill $\frac{99}{11} = 9$ orders, making a total of $9 + 11 = 20$ orders if they both work.

So for both of them working to fill one order would take:

$\frac{99}{20}$ hours.

To express in hours and minutes:

$\frac{99}{20} = \frac{80}{20} + \frac{19}{20} = 4 + \frac{3 \cdot 19}{3 \cdot 20} = 4 + \frac{57}{60}$

That's $4$ hours and $57$ minutes, since a sixtieth of an hour is one minute.