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.
- [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.
