# Lisa, an experienced shipping clerk, can fill a certain order in 10 hours. Tom, a new clerk, needs 13 hours to do the same job. Working together, how long will it take them to fill the order?

Dec 28, 2016

Both together will fill the order in $5.65 \left(2 \mathrm{dp}\right)$ hours.

#### Explanation:

In $1$ hour Lisa does $\frac{1}{10}$ th of the order.
In $1$ hour Tom does $\frac{1}{13}$ th of the order.

In $1$ hour both together do $\left(\frac{1}{10} + \frac{1}{13}\right) = \frac{13 + 10}{130} = \frac{23}{130}$ th of the order.

Both together do $\frac{23}{130}$ th part of the order in $1$ hour.

Therefore, both together will do full order in $\frac{1}{\frac{23}{130}} = \frac{130}{23} = 5.65 \left(2 \mathrm{dp}\right)$ hours. [Ans]