Question

A group of college students are volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Julian can paint a certain room in 3 hours. Mike can paint the same room in 7 hours. Write an equation that can be used to find how long it will take them working together to paint the room. Include equation

Answer 1

Consider their speeds:

J=1room/3hours
M=1room/7hours

Now, we want to combine their two speeds to paint one room:

Generally, number of rooms = (J's speed)(time) + (M's speed)(time). In this case,

1 room = (J)(time) + (M)(time)

1 room = (1/3)T + (1/7) T

Pull out the T: 1 = T (1/3 + 1/7)

1 = T (10/21)

So T = 21/10, or T = 21/10 hours. (2 and 1/10 hours).

Check:

In 21/10 hours, Julian painting 1 room/3 hours finishes 7/10 of the room.
In 21/10 hours, Mike painting 1 room/7 hours finishes 3/10 of the room.

So in 21/10 hours, they together paint the full 10/10 of the room!