12. Time and Motion

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$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.

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

Find the value of

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

$\editable{}$ hours $\editable{}$ minutes

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

Would the movie finish in the am or pm?

am

Apm

BComplete the statement:

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

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

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

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.

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?

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

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

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

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?