Question

One person can do a certain job in fifteen minutes, and another person can do the same job in thirty minutes. How many minutes will it take them to do the job together?

Answer 1

Each person works at their own rate.

1/15 and 1/30

The amount of work that they can do together is:

t/15+t/30

And we want to solve for when they can complete the job together:

t/15+t/30=1 making a common denominator

(t/15)(2/2)+t/30=1

(2t+t)/30=1 multiply both sides by 30

2t+t=30 combine like terms on left side

3t=30 divide both sides by 3

t=10

So it will take them 10 minutes to complete the job when working together.

Answer 2

‘A’ can do the job = 1/15 Job/minutes
‘B’ can do the same job = 1/30 Job/minutes
Both ‘A’ & ‘B’ can do the Job = 1/15+1/30
=(2+1)/30
=3/30=1/10 job/minutes
Both A & B can do the Job in 10 minute