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 $12$ hour system and the $24$ hour system.
12 hour system  24 hour system 
 Only uses numbers from $1$ to $12$ to describe the hour.
 Uses $am$ to refer to the time from midnight to $11{:}59$ in the morning and $pm$ to refer to the time from midday to $11{:}59$ in the evening.
  Uses numbers from $00$ to $23$ to describe the hour.
 $00$ is midnight.
 Hour is always $2$ digits (so $5$ is written as $05$).

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 $1am$ and $11am$: get rid of the $am$.
 If the hour is between $1pm$ and $11pm$: add $12$ to the hour, get rid of the $pm$.
 If the time is between $12am$ and $12{:}59am$: subtract $12$ and get rid of the $am$.
 If the time is between $12pm$ and $12{:}59pm$: get rid of the $pm$.
  If the hour is between $1$ and $11$: add an $am$.
 If the hour is between $13$ and $23{:}$ subtract $12$ from the hour, add a $pm$.
 If the time is between $00{:}00$ and $00{:}59$: add $12$ and add an $am$.
 If the time is between $12{:}00$ and $12{:}59$: add a $pm$.

Examples
 $6{:}30pm$ is $18{:}30$ in the $24$ hour format.
 $05{:}22$ is $5{:}22am$ in the $12$ hour format.
 $12{:}55am$ is $00{:}55$ in the $24$ hour format.
 $12{:}12$ is $12{:}12pm$ in the $12$ hour format.
Adding and subtracting times
When adding and subtracting times, always remember that there are $60$ minutes in an hour.
Example 1
How much time passes from $1{:}30pm$ to $5{:}15pm$?
First, find how much time is needed to get to the next hour:
The next hour is $2pm$. To get to $2pm$, you have to add $\textbf{30}$ minutes to $1{:}30pm$.
Then, find how much time is needed to get to $5pm$:
From $2pm$ to $5pm$, you have to add $52=\textbf{3}$ hours.
Find how much time is needed to get to $5{:}15pm$:
From $5pm$ to $5{:}15pm$, you have to add $\textbf{15}$ minutes.
Add all the times together:
$30$ minutes + $3$ hours + $15$ minutes = $3$ hours + $45$ minutes.
$\underline{3 \ \text{hours\ and} \ 45 \ \text{minutes}}$ passes from $1{:}30pm$ to ${5{:}15pm}$
Timetables
Timetables are used to organise schedules. They are often used in bus and train stations and they tend to use the $24$ 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 $X$ and $Y$.
ii) A family is at Cambridge and wants to arrive at Paddington before $2{:}30pm$. What is the latest train they can take?
station  arrival times 
train a  train b  train c 
Cambridge  $11{:}02$  $12{:}15$  $Y$ 
Tottenham  $12{:}27$  $X$  $14{:}37$ 
Paddington  $13{:}00$  $14{:}13$  $15{:}10$ 
Surrey  $14{:}05$  $15{:}18$  $16{:}15$ 
Part i)
The time it takes for the trains to go from Cambridge to Tottenham is always the same.
So, to find $X$ and $Y$, first find how long it takes Train A to go from Cambridge to Tottenham:
This is the same as finding the time from $11{:}02$ to $12{:}27$:
$11{:}02$ to $12{:}00$: $+\,\textbf{58}$ minutes
$12{:}00$ to $12{:}27$: $+\,\textbf{27}$ minutes
So, the time it takes to go from Cambridge to Tottenham is:
$58+27=85$ minutes
Convert this to minutes and hours:
$85$ minutes $=1$ hour and $25$ minutes
Add this time onto $12{:}15$ to find the value of $X$:
$12{:}15+1$ hour $+\,25$ minutes $=X$
$13{:}15+25$ minutes $=X$
$\underline{X=13{:}40}$
To find $Y$, subtract $1$ hour and $25$ minutes from $14{:}37$:
$14{:}371$ hour $\,25$ minutes $=Y$
$13{:}3725$ minutes $=Y$
$\underline{Y=13{:}12}$
Part ii)
First, convert $2{:}30pm$ to the $24$ hour format:
$2{:}30pm=14{:}30$
Look at the timetable to find the latest train that arrives at Paddington before $14{:}30$:
The latest train that arrives at Paddington before $14{:}30$ arrives at $14{:}13$.
This corresponds to the $12{:}15$ train at Cambridge.
The latest train that the family can take is train B.