Let's go through the problem step-by-step:
### Part a: Time Taken by the 0808 Bus from Birmingham to Coventry
1. Departure Time from Birmingham: The bus departs at 08:08 AM.
2. Arrival Time at Coventry: The bus arrives at 09:37 AM.
3. Calculate the Total Duration:
- Convert the departure and arrival times to minutes past midnight to simplify subtraction.
- Departure: 8 hours and 8 minutes past midnight is [tex]\( 8 \times 60 + 8 = 480 + 8 = 488 \)[/tex] minutes.
- Arrival: 9 hours and 37 minutes past midnight is [tex]\( 9 \times 60 + 37 = 540 + 37 = 577 \)[/tex] minutes.
4. Time Taken: The difference between the arrival and departure times is [tex]\( 577 - 488 = 89 \)[/tex] minutes.
- Therefore, the 0808 bus takes [tex]\(\boxed{89}\)[/tex] minutes to travel from Birmingham to Coventry.
### Part b: Latest Time Chris Should Leave His House
1. Work Start Time: Chris needs to be at work by 09:30 AM.
2. Walk Time:
- Walk from his house to the bus stop in Birmingham: 7 minutes.
- Walk from the bus stop in Coventry to his workplace: 15 minutes.
3. Total Walk Time: The total walk time is [tex]\( 7 + 15 = 22 \)[/tex] minutes.
4. Calculate the Latest Bus Arrival Time:
- Chris needs to be at work by 09:30 AM. He therefore needs to be at the Coventry bus stop 15 minutes earlier.
- Latest time to arrive at Coventry bus stop: [tex]\( 9:30 - 15 = 9:15 \)[/tex] AM.
5. Calculate the Latest Departure Time from Birmingham:
- The 0808 bus takes 89 minutes to get to Coventry.
- Thus, Chris needs to leave Birmingham 89 minutes before 09:15 AM.
- Convert 09:15 AM to minutes past midnight: [tex]\( 9 \times 60 + 15 = 540 + 15 = 555 \)[/tex] minutes.
- Latest departure time from Birmingham: [tex]\( 555 - 89 = 466 \)[/tex] minutes past midnight.
6. Calculate Latest Time to Leave His House:
- Chris needs to be at the Birmingham bus stop 7 minutes earlier.
- Latest time to leave the house: [tex]\( 466 - 7 = 459 \)[/tex] minutes past midnight.
7. Convert Back to Hours and Minutes:
- Convert 459 minutes past midnight back to hours and minutes: [tex]\( 459 \div 60 = 7 \)[/tex] hours and [tex]\( 459 \mod 60 = 39 \)[/tex] minutes.
So, the latest time Chris should leave his house is [tex]\(\boxed{7:39}\)[/tex] AM.
