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Your company pays employees time and a half for each hour they work overtime. An employee who earns [tex]\$30[/tex] per hour as regular pay worked [tex]3 \frac{1}{2}[/tex] hours of overtime one week and [tex]2 \frac{1}{4}[/tex] hours of overtime the next week.

1. How many hours of overtime did the employee work?

2. How much did the employee get paid for the overtime work?

Answer :

To find out how many hours of overtime the employee worked in total, we need to add the overtime hours from both weeks. The employee worked:

- [tex]\(3 \frac{1}{2}\)[/tex] hours the first week,
- and [tex]\(2 \frac{1}{4}\)[/tex] hours the second week.

First, let's convert these mixed numbers to improper fractions and then decimals for easy addition.

1. For the first week:
- [tex]\(3 \frac{1}{2}\)[/tex] hours can be written as [tex]\(3 + \frac{1}{2} = 3.5\)[/tex] hours.

2. For the second week:
- [tex]\(2 \frac{1}{4}\)[/tex] hours can be written as [tex]\(2 + \frac{1}{4} = 2.25\)[/tex] hours.

Next, we add these two amounts:

[tex]\[
3.5 \text{ hours} + 2.25 \text{ hours} = 5.75 \text{ hours}
\][/tex]

So, the employee worked a total of 5.75 hours of overtime.

Now, let's calculate how much the employee was paid for the overtime work. The employee’s regular pay rate is [tex]$30 per hour, and the overtime pay rate is time and a half. This means the overtime pay rate is:

\[ 1.5 \times 30 = 45 \text{ dollars per hour} \]

Finally, to find the total pay for the overtime work, we multiply the total overtime hours by the overtime pay rate:

\[ 5.75 \text{ hours} \times 45 \text{ dollars/hour} = 258.75 \text{ dollars} \]

Therefore, the employee got paid $[/tex]258.75 for their overtime work.

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