15.02 Time intervals

We work with time in almost every area of our life, so knowing how to add and subtract time, calculate the time between events, or even use a $24$24 hour clock are important. Let's look at some common ways we may need to work with time.

 

Adding and subtracting time

 

When we want to find the difference between times we can construct a subtraction expression in a similar way to how we usually subtract two numbers - but it's important to remember that there are $60$60 minutes in an hour, so we have to adjust our counting accordingly. People often forgot this in the calculations which can lead to errors. For example, the difference between $6$6 pm and $5:30$5:30 pm is $30$30 minutes. This is not the same as $6-5.3$6−5.3 which people commonly (and mistakenly) write, as this results in $0.7$0.7 (which they then interpret as $70$70 minutes - again, mistakenly).

Similarly, when adding time, once the total number of minutes reaches $60$60 minutes we add $1$1 to the hours instead.

 

Worked example

Example 1

Add $2$2 hours and $45$45 minutes to $5:25$5:25 pm.

Do: We could start by first adding the minutes $25+45$25+45 which is equal to $70$70 minutes. We can think of this as $60$60 minutes $+10$+10 minutes, which is $1$1 hour and $10$10 minutes. Now add the hours $5+2+1$5+2+1 and we get $8$8. So adding $2$2 hours and $45$45 minutes onto $5:25$5:25 pm takes us to $8:10$8:10 pm.

Reflect: Alternatively, we could view the problem more visually. Starting at $5:25$5:25 there are $35$35 minutes until $6:00$6:00. This leaves us with $2$2 hours and $10$10 minutes to add. First add the $10$10 minutes to reach $6:10$6:10 and then $2$2 hours to reach our final answer of $8:10$8:10 pm.

 

 

 

Practice questions

Question 1

Question 2

Question 3

 

Time between events

 

Worked example

Example 2

If a bus departs at $9:20$9:20 am and arrives at its final destination at $12:55$12:55 pm calculate the the length of the journey.

Think: We can do this by breaking the time down into smaller parts. This can be done visually as follows:

 

 

Do: Add the minutes together, remembering that once the minutes reach $60$60, we can add another hour.

From $9:20$9:20 am until $10:00$10:00 am	$=$=		$40$40 min
From $10:00$10:00 am to $12:00$12:00 pm	$=$=	$2$2 h
From $12:00$12:00 pm to $12:55$12:55 pm	$=$=		$55$55 min
Total:	$=$=	$2$2 h	$95$95 min

$95$95 minutes is $60$60 minutes + $35$35 minutes. ($1$1 hour and $35$35 minutes)

Thus, the journey was $3$3 hours and $35$35 minutes in duration.

 

Practice questions

question 4

question 5

 

Using the calculator for time calculations

We can also use our calculators to help with some of these calculations.

 

Worked example

Example 3

Calculate $3$3 hours $40$40 minutes - $1$1 hour $55$55 minutes.

Think: We can put it in the calculator using the DMS button like we would if we were to calculate angles.

Do:

Hence, the answer is $1$1 hour $45$45 minutes.

Reflect: Try the practice questions above again, this time using the calculator in this way. Do you get the same answers as before?

 

Time zones in Australia

Australia is divided into $3$3 time zones (shown below on the left-hand map). They are:

Eastern Standard Time (AEST): covering Queensland, New South Wales, Australian Capital Territory, Victoria and Tasmania.

Western Standard Time (AWST): covering Western Australia. ($2$2 hours behind AEST)

Central Standard Time (ACST): covering South Australia, Northern Territory. ($\frac{1}{2}$12​ an hour behind AEST)

The time zones become a bit more tricky during Daylight Savings because not all the states use it. Queensland, the Northern Territory and Western Australia stay on Standard Time. The map on the right shows that during Daylight Savings, Australia actually has $5$5 time zones!

 

During daylight savings, clocks are moved forward $1$1 hour from the standard time, so $8$8 am standard time would be $9$9 am in daylight savings time, $6$6 pm AEST would become $7$7 pm AEDT and so on.

Similarly, when we go from daylight savings time to standard time, clocks are moved back $1$1 hour, so $12$12 pm AEDT would be $11$11 am AEST and $14:22$14:22 AEDT would be $13:22$13:22 AEST.

 

Practice questions

Question 6

Question 7

Question 8

Question 9