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This is part of a bus timetable between Birmingham and Coventry.

\begin{tabular}{|l|l|l|l|l|l|l|}
\hline
Birmingham & 0705 & 0733 & 0808 & 0838 & 0905 & 0934 \\
\hline
Yardley & 0724 & 0753 & 0828 & 0858 & 0925 & 0954 \\
\hline
Solihull & 0744 & 0812 & 0847 & 0917 & 0944 & 1013 \\
\hline
Meriden & 0758 & 0826 & 0901 & 0931 & 0958 & 1027 \\
\hline
Coventry & 0834 & 0902 & 0937 & 1007 & 1034 & 1103 \\
\hline
\end{tabular}

a) How many minutes should the 0808 bus take to go from Birmingham to Coventry?
[tex]$\square$[/tex] minutes

b) Chris goes from Birmingham to Coventry by bus.
He takes 7 minutes to walk from his house to the bus stop in Birmingham. He takes 15 minutes to walk from the bus stop in Coventry to work.
Chris has to get to work by 9:30 am.
What is the latest time Chris should leave his house to get to work on time?
Answer: [tex]$\square$[/tex]

Sagot :

GinnyAnsweridn
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.
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