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Maths

Maths

Reading timetables

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Reading timetables 

​​In a nutshell

Timetables are used in many places in society. They are a useful and organised way of displaying schedules.



The 12 and 24 hour time system

Time is represented in two main formats: the 1212​ hour system and the 2424​ hour system.


12 hour system

24 hour system

  • Only uses numbers from 11​ to 1212​ to describe the hour.
  • Uses amam​ to refer to the time from midnight to 11:5911{:}59​ in the morning and pmpm​ to refer to the time from midday to 11:5911{:}59​ in the evening.
  • Uses numbers from 0000​ to 2323​ to describe the hour.
  • 0000​ is midnight.
  • Hour is always 22​ digits (so 55​ is written as 0505​).


​​Converting between the 12 and 24 hour formats

converting from 12 hour to 24 hour

Converting from 24 hour to 12 hour

  • If the hour is between 1am1am​ and 11am11am: get rid of the amam​.
  • If the hour is between 1pm1pm​ and 11pm11pm​: add 1212​ to the hour, get rid of the pmpm​.
  • If the time is between 12am12am​ and 12:59am12{:}59am: subtract 1212​ and get rid of the amam​.
  • If the time is between 12pm12pm​ and 12:59pm12{:}59pm: get rid of the pmpm​.
  • If the hour is between 11 and 1111​: add an amam​.
  • If the hour is between 1313​ and 23:23{:} subtract 1212​ from the hour, add a pmpm​.
  • If the time is between 00:0000{:}00​ and 00:5900{:}59: add 1212​ and add an amam​.
  • If the time is between 12:0012{:}00​ and 12:5912{:}59: add a pmpm​.


Examples
  • 6:30pm6{:}30pm​ is 18:3018{:}30​ in the 2424​ hour format.
  • 05:2205{:}22​ is 5:22am5{:}22am​ in the 1212​ hour format.
  • 12:55am12{:}55am is 00:5500{:}55in the 2424​ hour format.
  • 12:1212{:}12​ is 12:12pm12{:}12pmin the 1212​ hour format.



Adding and subtracting times

When adding and subtracting times, always remember that there are 6060​ minutes in an hour.


Example 1

How much time passes from 1:30pm1{:}30pm​ to 5:15pm5{:}15pm​?


First, find how much time is needed to get to the next hour:

The next hour is 2pm2pm​. To get to 2pm2pm​, you have to add 30\textbf{30}​ minutes to 1:30pm1{:}30pm​.


Then, find how much time is needed to get to 5pm5pm​:

From 2pm2pm​ to 5pm5pm​, you have to add 52=35-2=\textbf{3}hours.


Find how much time is needed to get to 5:15pm5{:}15pm​:

From 5pm5pm​ to 5:15pm5{:}15pm​, you have to add 15\textbf{15}​ minutes.


Add all the times together: 

3030minutes + 33 hours + 1515 minutes = 33 hours + 4545 minutes.


3 hours and 45 minutes\underline{3 \ \text{hours\ and} \ 45 \ \text{minutes}} passes from 1:30pm1{:}30pm to 5:15pm{5{:}15pm}



Timetables

Timetables are used to organise schedules. They are often used in bus and train stations and they tend to use the 2424​ hour time format.


Example 2

In the train timetable given, assume all trains take the same amount of time to make the same journey.

i) Find the values of XX​ and YY​.

ii) A family is at Cambridge and wants to arrive at Paddington before 2:30pm2{:}30pm. What is the latest train they can take?


station

arrival times

train a

train b

train c

Cambridge

11:0211{:}02​​

12:1512{:}15​​

YY​​

Tottenham

12:2712{:}27​​

XX​​

14:3714{:}37​​

Paddington

13:0013{:}00​​

14:1314{:}13​​

15:1015{:}10​​

Surrey

14:0514{:}05​​

15:1815{:}18​​

16:1516{:}15​​


Part i)

The time it takes for the trains to go from Cambridge to Tottenham is always the same. 

So, to find XX​ and YY, first find how long it takes Train A to go from Cambridge to Tottenham:

This is the same as finding the time from 11:0211{:}02 to 12:2712{:}27:

11:0211{:}02to 12:0012{:}00: + 58+\,\textbf{58} minutes


12:0012{:}00to 12:2712{:}27: + 27+\,\textbf{27} minutes


So, the time it takes to go from Cambridge to Tottenham is:

58+27=8558+27=85minutes


Convert this to minutes and hours:

8585minutes =1=1 hour and 2525 minutes


Add this time onto 12:1512{:}15 to find the value of XX:

12:15+112{:}15+1hour + 25+\,25