Question

Working alone at their respective constant rates, machine A and machine B can fill a certain order in 3 hours and 6 hours, respectively. If the two machines work simultaneously at their respective constant rates, how many hours does it take the two machines to fill?

Answer 1

Answer: 2 hours

Explanation:

Given : Working alone at their respective constant rates, machine A and machine B can fill a certain order in 3 hours and 6 hours, respectively.

Let t be the time taken by both of them working together.

Then, according to the question, we have

`(1)/(t)=(1)/(3)+(1)/(6)\\\\\Rightarrow(1)/(t)=(2+1)/(6)\ \ [\because\ L.C.M. (3,6)=6]\\\\\Rightarrow(1)/(t)=(3)/(6)=(1)/(2)\\\\\Rightarrow t=2`

Hence, it will take 2 hours by the two machines .