# Maria, an experienced shipping clerk, can fill a certain order in 14 hours. Jim, a new clerk, needs 17 hours to do the same job. Working together, how long will it take them to fill the order?

May 21, 2018

About $7 \frac{2}{3}$ hours or $7$ hours and $40$ minutes

#### Explanation:

Consider how much of the task each would complete in one hour:

Maria will complete $\frac{1}{14}$ of the order in one hour.
Jim will complete $\frac{1}{17}$ of the order in one hour.

So if they work together, then after one hour:

$\frac{1}{14} + \frac{1}{17}$ of the order will have been completed.

$= \frac{17 + 14}{14 \times 17}$

$= \frac{31}{238}$

To complete the whole task, a whole, or $1 \mathmr{and} \frac{238}{238}$ will take:

$\frac{238}{238} \div \frac{31}{238}$

$= 1 \times \frac{238}{31}$

$= 7 \frac{21}{31}$ hours

$= 7$ hours and $40.6$ minutes