Question

Javier and Brianna both have summer jobs working at Honeybee Ice Cream. Javier makes $15 per hour, and he has already earned a total of $270 this summer. Brianna is starting today, and she will be making $18 per hour as a new manager. Javier and Brianna work the same schedule.
Which equation can you use to find h, the number of hours of work it will take for Brianna and Javier to have earned the same amount of money?
How many hours of work will it take for Brianna and Javier to have earned the same amount of money?

Answer 1

To find the number of hours \( h \) it will take for Brianna and Javier to have earned the same amount of money, we start by setting up the equations for their total earnings.

Javier's earnings:
- He has already earned $270, and he makes $15 per hour, so after \( h \) hours, his total earnings can be expressed as:
\[
\text{Earnings}_J = 270 + 15h
\]

Brianna's earnings:
- She just started and hasn't earned anything yet, but she will earn $18 per hour. After \( h \) hours, her total earnings can be expressed as:
\[
\text{Earnings}_B = 18h
\]

To find when they have the same earnings, we can set their total earnings equal to each other:
\[
270 + 15h = 18h
\]

Now, we can solve this equation for \( h \):

1. First, isolate \( h \) by subtracting \( 15h \) from both sides:
\[
270 = 18h - 15h
\]
\[
270 = 3h
\]

2. Now, divide both sides by 3 to solve for \( h \):
\[
h = \frac{270}{3} = 90
\]

So, it will take **90 hours** of work for Brianna and Javier to have earned the same amount of money.