Question

Three postal workers can sort a stack of mail in 30 minutes 45 minutes, and 90 minutes, respectively Find how long it takes them to sort the mail if all three work together

Answer 1

Person 1: They can sort the mail in 30 minutes, so they do 1/30th of the job in one minute.

Person 2: They can sort the mail in 45 minutes, so they do 1/45th of the job in one minute.

Person 3: They can sort the mail in 90 minutes, so they do 1/90th of the job in one minute.

Together, they do (1/30 + 1/45 + 1/90)th of the job in one minute.

1/30 + 1/45 + 1/90 = 3/90 + 2/90 + 1/90 = 6/90

So they do 6/90 of the job together in 1 minute.

If "t" is the time it takes them working together to do the job, then we need to solve

   6/90 · t = 1     (that's 1 for 1 whole job)

Solving that, you get t = 90/6 = 15

So, it'd take them 15 minutes working together to get that job done.