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