Question

Three postal workers can sort a stack of mail in 40 ​minutes, 30 ​minutes, and 120 ​minutes, respectively. Find how long it takes them to sort the mail if all three work together.

The time it takes for all three to complete the job is _________ minutes.

Answer 1

The No1 worker can sort a stack of mail in 40 minutes, The No2 worker can sort a stack of mail in 30 minutes and The No3 worker can sort a stack of mail in 120 minutes.

In 40 min the No1 worker can do 1 work

so, in 1 min the No1 worker can do 1/40 work

In 30 min the No1 worker can do 1 work

so, in 1 min the No1 worker can do 1/30 work

In 120 min the No1 worker can do 1 work

so, in 1 min the No1 worker can do 1/120 work

If the 3 workers work together,

they can do in 1 minute = (1/40 + 1/30 + 1/120 ) work

= 1/15 work

they can do 1/15 work in 1 minute

so, they can do full 1 work in = 15 minutes

Therefore, The time it takes for all three to complete the job is 15 minutes.