How to do the how long will it take two people to paint a room problem?

Two people painting a room:

Let's example: Mark takes 3 hours, Jane takes 5 hours, to paint the same room.

Let x = the amount of the room each person paints in a given amount of time.

So, Mark's contribution is represented by x/3

Jane's contribution is represented by x/5

Together, they paint one entire room, so our equation will equal ... 1.

[Our working equation] x/3 + x/5 = 1

[Find common denominator] 5x/15 + 3x/15 = 1

[add fractions] 8x/15=1

[solve for x] 8x=15

x=15/8 or 1 7/8 hours. They can paint the room together in 1 7/8 hours.