3.04 12 and 24 hour time

There are two main ways we represent time over a day. 24 hour time represents time as one block of 24 hours. 12 hour time represents a day as two blocks of 12 hours each. The hours before midday add an "am" to show it's the morning and the hours after midday add on a "pm" so we know it's the afternoon.

There is also variation in how 12 and 24 hour time is displayed. 12 hour time may use "am", "a.m.", "AM" or similar variations, while 24 hour time could represent 03:15 as 3:15 or 0315 which is more common in the military.

Below is a diagram showing the conversion between 12 and 24 time. In all cases the number of minutes will be the same.

The conversions between the different units of time are:

Time calculations are similar to our normal addition and subtraction so we can use similar strategies. However, we will also use these time unit conversions, such as 60 minutes in an hour and 24 hours in a day.

Examples

Example 1

Write 9 days to hours.

Worked Solution

Create a strategy

Use the image below to convert days in hours:

Apply the idea

\displaystyle 9 \text{ days}	\displaystyle =	\displaystyle 9 \times 24 \text { hours}	Multiply by 24
	\displaystyle =	\displaystyle 216 \text{ hours}	Evaluate

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Example 2

Which of the following represents 30 minutes after 11:40 pm?

A

12:10 am

B

11:10 pm

C

11:70 pm

D

12:10 pm

Worked Solution

Create a strategy

When adding times, if the minutes add to 60 or more increase the number of hours. The time will change between pm to am whenever the hour changes from 11 to 12.

Apply the idea

Add the 30 minutes by adding 20 and then 10 minutes.11:40 \text{ pm} + 20 \text{ minutes} = 12:00 \text { am}

Add the remaining 10 minutes:12:00 \text{ am} + 10 \text{ minutes} = 12:10 \text { am}

30 minutes after 11:40 am will be 12:10 am, option A.

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Example 3

Kate leaves her home at 11:15 am to visit her grandmother in a different state. She arrives at her grandmother's house at 5:15 pm. How long was Kate's trip in hours?

Worked Solution

Create a strategy

Since both times have the same number of minutes, so we can focus on the difference between the hours. Find difference between 11:00 am and 5:00 pm.

Apply the idea

The number of hours from 11:00 am to 12:00 midday is 1. The number of hours between 12:00 midday and 5:00 pm is 5.

\displaystyle \text{Length of trip}	\displaystyle =	\displaystyle 1 + 5	Add the hours
	\displaystyle =	\displaystyle 6 \text{ hours}	Evaluate

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