# Calculating pay at two different rates

### Question:

Bill makes $24 per hour for a standard 40 hour work week. He earns time-and-a-half for every hour worked over 40 hours during that week. If Bill earned$1140 last week (ignoring all taxes and deductions), how many overtime hours did he work?

$$\text{Regular: } 40hrs * 24 = 960$$
The second step is to figure out how much he made as overtime. If Bill earned $1140 total, and$960 of that came from his regular hours, then obviously the rest was overtime:
$$\text{Overtime: } 1140 - 960 = 180$$
Now that we know how much he made in overtime we can calculate how many hours he worked. Since multiplying his hours times the hourly rate will give us $180, we can express that in an equation as well. Remember that he's now earning 1.5 times his regular wage (since he qualified for time-and-a-half overtime pay). $$(hours)*(24)*(1.5)=180$$ $$hours*36=180$$ $$hours=\frac{180}{36}=5$$ Bill must have worked 5 hours of overtime to earn a total of$1140 for the week.