Question

Three postal workers can sort a stack of mail in 20 ​minutes, 30 ​minutes, and 60 ​minutes, respectively. Find how long it takes them to sort the mail if all three work together.

Answer 1

Answer: 10 minutes

Step-by-step explanation:

Given : Three postal workers can sort a stack of mail in 20 ​minutes, 30 ​minutes, and 60 ​minutes, respectively.

Let T be the time taken by all of them when they working together.

Then , we have the following equation :-

$\dfrac{1}{T}=\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{60}\\\\\Rightarrow\dfrac{1}{T}=\dfrac{3+2+1}{60}\\\\\Rightarrow\dfrac{1}{T}=\dfrac{6}{60}=\dfrac{1}{10}\\\\\Rightarrow T=10$

Hence, the time taken by all of them when they working together = 10 minutes.