Chapter overview Maths

Types of numbers

Number calculations

Fractions, decimals and percentages

Algebraic manipulation

Formulae and equations

Straight line graphs

Other graphs

Ratio

Proportion

Rates of change

Shapes

Properties of shapes

Measures

Lines and angles

Drawing shapes

Trigonometry

Probability

Statistics

Maths  0%

Summary

## ​​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.

#### 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 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.

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.

$30$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?

#### train c

Cambridge

$11{:}02$​​

$12{:}15$​​

$Y$​​

Tottenham

$12{:}27$​​

$X$​​

$14{:}37$​​

$13{:}00$​​

$14{:}13$​​

$15{:}10$​​

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 $+\,25$