Question

Janet an experienced shipping clerk can fill a certain order in 5 hours . Tom a new clerk needs 8 hours to do the same job. working together how long will it take them to fill the order

Answer 1

Janet can fill a certain order in 5 hours, therefore she performs 1/5 of the order within 1 hour.

Tom needs 8 hours to do the same job, therefore he performs 1/8 of the order within 1 hour.

Working together, they make 1/5 + 1/8 orders within 1 hour.

Let t mean the number of hours they need. Then we have equation:

$\left(\dfrac{1}{5}+\dfrac{1}{8}\right)t=1\\\\_{\text{use}\ \frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}}\\\\\dfrac{(1)(8)+(1)(5)}{(5)(8)}t=1\\\\\dfrac{8+5}{40}t=1\\\\\dfrac{13}{40}t=1\ \ \ \ |\text{multiply both sides by 40}\\\\13t=40\ \ \ \ |\text{divide both sides by 13}\\\\t=\dfrac{40}{13}\\\\t=3\dfrac{1}{13}\\\\Answer:\ 3\dfrac{1}{13}h=3h\ \dfrac{60}{13}min\approx3h\ 5min$