topic badge

12.02 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$65.3 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.




$60$60 minutes makes $1$1 hour


Practice questions

Question 1

Find the value of

$3$3 hours $3$3 minutes $+$+ $3$3 hours $29$29 minutes

  1. $\editable{}$ hours $\editable{}$ minutes

Question 2

James went to a movie at $11:50$11:50 am. The movie went for $1$1 hour and $10$10 minutes.

  1. Would the movie finish in the am or pm?




  2. Complete the statement:

    The movie finishes at $\editable{}$$:$:$\editable{}$$\editable{}$ pm.

Question 3

Evaluate $6$6 hours $10$10 minutes $-$ $2$2 hours $30$30 minutes.

  1. $\editable{}$ hour(s) $\editable{}$ minute(s)


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

A song clip starts playing at $7$7:$55$55 pm and finished at $8$8:$11$11 pm. How long is the song clip in minutes?

question 5

A taxi departs at 13:32 from Sydney and arrives at 20:14 at Melbourne. How long did the taxi take for the trip?

  1. The trip took $\editable{}$ hour(s) and $\editable{}$ minute(s)


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.


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?




calculate time intervals, such as time between, time ahead, time behind

What is Mathspace

About Mathspace