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Answer :
We are given that the total journey time from Reading to Worle is the same for every departure and arrival pair. We can use one of the provided journeys to determine this constant time.
1. First, consider the journey from Reading at [tex]$11{:}05$[/tex] to Worle at [tex]$12{:}55$[/tex]. Convert these times into minutes after midnight:
- For [tex]$11{:}05$[/tex], the calculation is
[tex]$$11 \times 60 + 5 = 660 + 5 = 665 \text{ minutes.}$$[/tex]
- For [tex]$12{:}55$[/tex], the calculation is
[tex]$$12 \times 60 + 55 = 720 + 55 = 775 \text{ minutes.}$$[/tex]
2. The total journey time in minutes is then calculated as:
[tex]$$775 - 665 = 110 \text{ minutes.}$$[/tex]
3. Now, consider the Reading departure at [tex]$11{:}30$[/tex]. Converting that time into minutes gives:
[tex]$$11 \times 60 + 30 = 660 + 30 = 690 \text{ minutes.}$$[/tex]
4. Since the journey always takes [tex]$110$[/tex] minutes, add this duration to the [tex]$11{:}30$[/tex] departure time:
[tex]$$690 + 110 = 800 \text{ minutes.}$$[/tex]
5. Convert [tex]$800$[/tex] minutes back into hours and minutes. We first determine the number of full hours by dividing by [tex]$60$[/tex]:
[tex]$$800 \div 60 = 13 \text{ hours (since }13 \times 60 = 780\text{)}.$$[/tex]
The remaining minutes are:
[tex]$$800 - 780 = 20 \text{ minutes.}$$[/tex]
Thus, the arrival time is [tex]$13{:}20$[/tex].
Therefore, the time that goes in the gap is:
[tex]$$\boxed{13:20}$$[/tex]
1. First, consider the journey from Reading at [tex]$11{:}05$[/tex] to Worle at [tex]$12{:}55$[/tex]. Convert these times into minutes after midnight:
- For [tex]$11{:}05$[/tex], the calculation is
[tex]$$11 \times 60 + 5 = 660 + 5 = 665 \text{ minutes.}$$[/tex]
- For [tex]$12{:}55$[/tex], the calculation is
[tex]$$12 \times 60 + 55 = 720 + 55 = 775 \text{ minutes.}$$[/tex]
2. The total journey time in minutes is then calculated as:
[tex]$$775 - 665 = 110 \text{ minutes.}$$[/tex]
3. Now, consider the Reading departure at [tex]$11{:}30$[/tex]. Converting that time into minutes gives:
[tex]$$11 \times 60 + 30 = 660 + 30 = 690 \text{ minutes.}$$[/tex]
4. Since the journey always takes [tex]$110$[/tex] minutes, add this duration to the [tex]$11{:}30$[/tex] departure time:
[tex]$$690 + 110 = 800 \text{ minutes.}$$[/tex]
5. Convert [tex]$800$[/tex] minutes back into hours and minutes. We first determine the number of full hours by dividing by [tex]$60$[/tex]:
[tex]$$800 \div 60 = 13 \text{ hours (since }13 \times 60 = 780\text{)}.$$[/tex]
The remaining minutes are:
[tex]$$800 - 780 = 20 \text{ minutes.}$$[/tex]
Thus, the arrival time is [tex]$13{:}20$[/tex].
Therefore, the time that goes in the gap is:
[tex]$$\boxed{13:20}$$[/tex]
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