## 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?

### Answer:

We can divide Bill's earnings into two categories. He earned a certain amount during his regular time and a certain amount extra in overtime. The first step is to calculate how much money Bill Tupper made during his regular 40 hours:

$$ \text{Regular: } 40hrs * $24 = $960 $$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.