Let's go through each part of the question step by step.
### Part a
Jim catches the 1221 train from Preston and arrives in Nuneaton 7 minutes late.
The scheduled arrival time in Nuneaton is 13:54 (1354 in 24-hour format). Given that he is 7 minutes late, we need to calculate his actual arrival time.
[tex]\[ \text{Actual arrival time} = 1354 + 7 \][/tex]
Since 60 minutes make an hour, when we add 7 minutes to 54 minutes, we get:
[tex]\[ 54 + 7 = 61 \text{ minutes} \][/tex]
Since 61 minutes is equivalent to 1 hour and 1 minute, we add the extra hour to 13:
[tex]\[ 1354 + 7 = 1361 \][/tex]
This converts to 14:01 in 24-hour format.
So, Jim arrives in Nuneaton at 14:01.
### Part b
We need to calculate the journey time from Preston to Nuneaton for Jim.
The departure time from Preston is 12:21 (1221 in 24-hour format) and the scheduled arrival time in Nuneaton is 13:54 (1354 in 24-hour format).
To find the journey time in minutes:
[tex]\[ \text{Journey time} = 1354 - 1221 \][/tex]
Let's break down the subtraction:
First, consider the hours part:
[tex]\[ 13 - 12 = 1 \text{ hour} \][/tex]
Then, consider the minutes part:
[tex]\[ 54 - 21 = 33 \text{ minutes} \][/tex]
Thus, the total journey time is:
[tex]\[ 1 \text{ hour and } 33 \text{ minutes} \][/tex]
Which translates to:
[tex]\[ 1 \text{ hour} \times 60 \text{ minutes/hour} + 33 \text{ minutes} = 60 + 33 = 93 \text{ minutes} \][/tex]
So, the journey time from Preston to Nuneaton is 93 minutes.
### Part c
Vikram catches the 08:40 (0840 in 24-hour format) train from Preston and arrives in Nuneaton on time at 10:28 (1028 in 24-hour format). He has a job interview which lasts for 3 hours and 30 minutes.
First, let's convert the interview duration to minutes:
[tex]\[ 3 \text{ hours} \times 60 \text{ minutes/hour} + 30 \text{ minutes} = 180 + 30 = 210 \text{ minutes} \][/tex]
To find the time Vikram gets back to Nuneaton station, we add the interview duration to his arrival time:
[tex]\[ \text{Back to station time} = 1028 + 210 \][/tex]
Let's break this down:
First, add 210 minutes to the minutes part of 10:28:
[tex]\[ 28 + 210 = 238 \text{ minutes} \][/tex]
Since 238 minutes is equivalent to 3 hours and 58 minutes (because 238 ÷ 60 = 3 remainder 58):
[tex]\[ 238 \text{ minutes} = 3 \text{ hours and } 58 \text{ minutes} \][/tex]
So, we add these 3 hours to the 10 hours:
[tex]\[ 10 + 3 = 13 \][/tex]
And we add the remaining 58 minutes:
So, the time will be:
[tex]\[ 13:28 + 0:58 = 13:86 \][/tex]
And since 86 minutes is 1 hour and 26 minutes:
[tex]\[ 1386 = 14:26 \][/tex]
Thus, Vikram gets back to Nuneaton station at 14:26 (1426).
Compare this to the time of the next train to Milton Keynes, which leaves Nuneaton at 13:54 (1354).
By comparison, we note that 1426 is after 1354, so Vikram is not back in time to catch the 1354 train to Milton Keynes.
