Unit 18 Section 3 : Problems with mixed units

Often we see a mixture of units in questions about distance, speed and time. This section looks at how to deal with this situation, including how to write times in different ways.

Writing times in different ways
The time 3.5 hours can also be written as 3 hours and 30 minutes.
Being able to convert between these two forms can be useful when answering questions.

To convert from "decimal hours" to "hours and minutes", first separate the whole number; this is the number of hours.
Next, multiply the decimal part by 60 to find the number of minutes.

Example
Convert 12.4 hours to hours and minutes.
The whole number is 12, so the answer will include 12 hours.
The decimal part is 0.4, and we multiply this by 60 to get 24. This is the number of minutes.
12.4 hours can also be written as 12 hours and 24 minutes.

To convert from "hours and minutes" to "decimal hours", first separate the number of hours; this is the whole number.
Next, divide the number of minutes by 60 to find the decimal part.

Example
Convert 3 hours 21 minutes to decimal hours.
There are 3 hours, so the whole number part of the answer will be 3.
We divide 21 by 60 to get the decimal part to the answer: 0.35
3 hours 21 minutes can also be written as 3.35 hours.

Example Question
James travels for 4 hours and 39 minutes at 25.6 km/h.

How far has he travelled, to the nearest kilometre?
To find distance, we need to multiply speed by time, so we need to convert the time to a decimal format.
4 hours and 39 minutes gives 4 as the whole number part and 0.65 as the decimal part (becuase 39 ÷ 60 = 0.65).
Distance = speed × time = 25.6 km/h × 4.65 hours = 119.04 km
James has travelled 119 km.

Practice Questions

What is 3.4 hours in hours and minutes?

What is 2 hours and 57 minutes in decimal hours?

Jonah cycles for 5.06 km at 4.4 km/h. How long does it take in hours and minutes?

Exercises

Question 1
Convert the following times from hours and minutes to decimal hours, rounding to 2 decimal places where necessary:

(a) 1 hour 40 minutes	hours
(b) 3 hours 10 minutes	hours
(c) 1 hour 6 minutes	hours
(d) 2 hours 18 minutes	hours
(e) 3 hours 5 minutes	hours
(f) 6 hours 2 minutes	hours
(g) 1 hour 7 minutes	hours
(h) 2 hours 23 minutes	hours

Question 2
Change the following times to hours and minutes:

(a) 1.25 hours	1 hr mins
(b) 1.2 hours	1 hr mins
(c) 3.7 hours	3 hrs mins
(d) 4.4 hours	4 hrs mins
(e) 1.45 hours	1 hr mins
(f) 3.65 hours	3 hrs mins