To determine if Lee finishes the last job before 1 pm, we need to calculate the start and end times of each job, including the break time.
1. Starting Time:
- Lee starts his first job at 9 am.
2. Service Time:
- The service takes [tex]\(1.5\)[/tex] hours. To convert this to minutes:
[tex]\[
1.5 \, \text{hours} \times 60 \, \text{minutes/hour} = 90 \, \text{minutes}
\][/tex]
- The service ends at:
[tex]\[
9 \, \text{am} + 90 \, \text{minutes} = 10:30 \, \text{am}
\][/tex]
3. Oil Change:
- The oil change takes [tex]\(\frac{3}{4}\)[/tex] of an hour. To convert this to minutes:
[tex]\[
\frac{3}{4} \, \text{hours} \times 60 \, \text{minutes/hour} = 45 \, \text{minutes}
\][/tex]
- The oil change ends at:
[tex]\[
10:30 \, \text{am} + 45 \, \text{minutes} = 11:15 \, \text{am}
\][/tex]
4. Break Time:
- Lee takes a break of 30 minutes. The break ends at:
[tex]\[
11:15 \, \text{am} + 30 \, \text{minutes} = 11:45 \, \text{am}
\][/tex]
5. Replace Headlight:
- Replacing the headlight takes 20 minutes. The headlight replacement ends at:
[tex]\[
11:45 \, \text{am} + 20 \, \text{minutes} = 12:05 \, \text{pm}
\][/tex]
6. Checking Against 1 pm:
- To confirm if 12:05 pm is before 1 pm, convert 1 pm to minutes from the start of the day.
[tex]\[
1 \, \text{pm} = 13 \, \text{hours} \times 60 \, \text{minutes/hour} = 780 \, \text{minutes from 12 am}
\][/tex]
- 12:05 pm in minutes from the start of the day is:
[tex]\[
12 \, \text{hours} \times 60 \, \text{minutes/hour} + 5 \, \text{minutes} = 725 \, \text{minutes from 12 am}
\][/tex]
Since 725 minutes (12:05 pm) is indeed before 780 minutes (1 pm), Lee will finish the last job before 1 pm. Hence, the answer is True.
