Seth paints houses for a fee of $39 and an hourly rate of $13. Malcolm paints houses for a fee of $55 and an hourly rate of $11.

In how many hours will Seth and Malcolm earn the same amount?

Let's begin by putting together some equations:

Seth has charges $39 and then $13 per hour. Since "hour" is our variable, let's write that as $13h where h = the number of hours.

Seth = 39 + 13h, $39 plus $13 times the number of hours

Malcolm charges $55 and then $11 per hour. So:

Malcolm = 55 + 11h, $55 plus $11 times the number of hours

Our goal is to find out how many hours both have to work before they charge the same amount. So let's set our Seth and Malcolm equations equal to one another.

39 + 13h = 55 + 11h, because we want to solve for h to see the number of hours.

First let's subtract 39 from each side:

(39 + 13h) - 39 = (55 + 11h) - 39

13h = 16 + 11h

Now let's subtract 11h from each side:

(13h) - 11h = (16 + 11h) - 11h

2h = 16

Simplify and solve for h by dividing each side by two:

(2h) / 2 = (16) / 2

h = 8

So Malcolm and Seth would have to work for 8 hours before both earn the same amount. After 8 hours, Seth would earn more than Malcolm. Before 8 hours, Malcolm would earn more than Seth.