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?

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.