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.

​​Converting between the 12 and 24 hour formats

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 $$5-2=\textbf{3}$$​ 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?

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 $$14{:}37$$:

​$$14{:}37-1$$ hour $$-\,25$$ minutes $$=Y$$​

​$$13{:}37-25$$ 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.