# 12.02 Time intervals

Lesson

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.

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.

Remember!

$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?

am

A

pm

B
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.

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?

### Outcomes

#### ACMEM078

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