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6.01 Units of time


Seconds, minutes, and hours all are units of time. The smallest unit of the three is seconds. A second is approximately the time between 2 heartbeats. it takes $60$60 seconds to make up $1$1 minute, and it takes $60$60 minutes to make up an hour.

Knowing this relationship helps us to convert between seconds, minutes, and hours.

We can use multiplication and division to change between them.

If we want to know how many seconds are in $5$5 minutes of time, we can multiply that by $60$60 seconds because there are $60$60 seconds for each minute. $5\times60=300$5×60=300, so there are $300$300 seconds in $5$5 minutes.


Watch this video to see a couple of examples.

$1$1 Week $=$= $7$7 Days
$1$1 Day $=$= $24$24 Hours
$1$1 Hour $=$= $60$60 Minutes
$1$1 Minute $=$= $60$60 Seconds


Practice questions

Question 1

Write the missing number in the box.

  1. There are $\editable{}$ seconds in $1$1 minute.

Question 2

It takes around $300$300 minutes to drive from Sydney to Thredbo.

How many hours is this?

Question 3

Han boils an egg for $360$360 seconds.

  1. How many minutes is this?


Worked example

If it took $9$9 hours and $15$15 minutes to drive to Sydney, how many minutes did it take?  

Think: Firstly calculate how many minutes are in $9$9 hours.  

We know that $1$1 hour  = $60$60 minutes, so to calculate the number of minutes in 9 hours we need to multiply

$9$9 x $60$60 = $540$540 minutes

So there are $540$540 minutes in $9$9 hours.

Next we need to add $540$540 minutes and $15$15 minutes

Do: Calculate $540$540 + $15$15 = $555$555


So it took $555$555 minutes to drive to Sydney.


Don't forget to write the units.


Solving different types of time problems

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 hour clock are important.   Let's look at some common ways we may need to work with time.  

In this video, you'll see how to calculate elapsed time, how to add two blocks of time together, as well as how to work out how long you might need to binge-watch your favourite tv show!


Practice questions

Question 4

Find the value of

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

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

Question 5

Find the value of

$2$2 hours $50$50 minutes $+$+ $3$3 hours $40$40 minutes

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


Subtracting time

When subtracting time in hours and minutes it can be tricky because there are $60$60 minutes in and hour so we can't work it out like we would normal numbers. But we can still create an algorithm to evaluate the subtraction but we need to keep in mind $1$1 hour $=$=$60$60 minutes.


Practice questions

Question 6

Find the value of 

$11$11 hours $-$ $43$43 minutes

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

Question 7

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

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


Using the calculator for time calculations

Most scientific calculators will have a button that looks like this:  

This is the "degrees, minutes, seconds" (DMS) button that we can use for angles and time calculations.

For example, if we wanted to calculate $3$3 hours $40$40 minutes - $1$1 hour $55$55 minutes, we can put it in the calculator using the DMS button like we would if we were to calculate angles.


We read the answer to be $1$1 hour $45$45 minutes.

Try the examples above again using the calculator.


The 24 hour clock

Sometimes you may need to know how to use $24$24 hour time, so this video shows you how to do that. 


Practice questions

Question 8

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)

Question 9

A train ride between two cities takes $9$9 hours and $57$57 minutes. On a train ride between these cities, if you leave one city at $23$23$:$:$44$44, at what time will you arrive at the other city?

Give your answer in $24$24 hour time.

  1. Time of arrival $=$= $\editable{}$$:$:$\editable{}$



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