# 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.

### 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.

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

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?

### 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

If it is $16$16:$14$14 in Sydney in Daylight Savings Time, what time would it be in Eastern Standard Time?

1. $16$16:$14$14 AEDT would be $\editable{}$:$\editable{}$ AEST.

##### Question 7

If it is $14$14:$35$35 in Sydney in Eastern Standard Time, what time would it be in Daylight Savings Time?

1. $14$14:$35$35 AEST would be $\editable{}$:$\editable{}$ AEDT.

##### Question 8

Complete the table to show the time in each time zone.

1. WST CST EST
$\editable{}$$::\editable{} 55::2525 \editable{}$$:$:$\editable{}$

$5$5$:$:$11$11 $\editable{}$$::\editable{} \editable{}$$:$:$\editable{}$
$\editable{}$$::\editable{} \editable{}$$:$:$\editable{}$ $12$12$:$:$25$25
$\editable{}$$::\editable{} 77::1717 \editable{}$$:$:$\editable{}$

##### Question 9

Luke and Maria board a train at $7$7:$58$58 PM on Saturday from Sydney, New South Wales towards Adelaide, South Australia.

1. If the trip to Adelaide took $20$20 hours and $22$22 mins then they arrived on $\editable{}$:$\editable{}$ PM Sunday in Adelaide local time.

2. Luke boards a train from Adelaide, South Australia at $5$5:$45$45 PM on Sunday to Darwin, Northern Territory. If his trip took $28$28 hours and $36$36 mins, then he arrived at $\editable{}$:$\editable{}$ PM Monday Darwin local time.

3. Maria boards a train from Adelaide, South Australia at $4$4:$55$55 PM Sunday towards Perth, Western Australia. If the trip took her $19$19 hours and $20$20 mins, then she arrived at $\editable{}$:$\editable{}$ AM in Perth local time.

### Outcomes

#### ACMEM078

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