Question

It takes a new mail carrier 4 hours to deliver the mail on route a. It takes an experienced mail carrier 3 hours to do the same job. How long would it take if they worked together?

Answer 1

Answer: $\frac{12}{7}\ \text{hours}$

Step-by-step explanation:

Given

New mail carrier takes 4 hours for delivery i.e.

New mail carrier completes $\frac{1}{4}$ part of work in 1 hour

Old mail carrier takes 3 hours for delivery  i.e.

mail carrier completes $\frac{1}{3}$  part of work in 1 hour

If they work together, they complete the work in x hours i.e.

$\Rightarrow \dfrac{1}{x}=\dfrac{1}{4}+\dfrac{1}{3}\\\Rightarrow \dfrac{1}{x}=\dfrac{3+4}{12}\\\Rightarrow x=\dfrac{12}{7}\ \text{hours}$