QTS Numeracy Model Solutions – Test 2, Q24

In this series of blog posts, we look at some of the detailed methods that you could use to tackle the questions on the QTS Numeracy practice papers from the Department for Education.

In this post, we look at question 24 from practice test 2. The full practice paper can be downloaded here​.

The Question

A teacher plans a school trip to Brussels, which involves using a ferry from Ostend. The teacher wants to be in Ostend no later than 18:00. She expects their coach to travel from Brussels to Ostend, a distance of 120km, at an average of 50 miles per hour.

Using the approximation of 5 miles equals 8 kilometres, what is the latest time that the coach should leave Brussels? Give your answer using the 24-hour clock.

Worked Solution

This is a question that combines time and measurement conversions and requires several stages of calculation.

It is easy to get lost in questions like this. The best approach is often to make sure you are crystal clear about what you are trying to find, and see what steps you can take to achieve that.

In this case, you need to know the latest time that the coach can leave Brussels. To work this out, you will first need to know how long the journey will take and then subtract this from 18:00.

To work out the time a journey takes, you need to divide the total distance by the average speed. You are given both of these pieces of information in the question, but they are not given in the same units – the distance is given in kilometres, and the average speed is given in miles per hour.

Before you can calculate the journey time, you need to convert both of these measurements into the same units. It doesn’t matter whether you put both into kilometres or both into miles, as long as they are the same.  

You are given the conversion 5 miles = 8 kilometres. To use this conversion to convert from miles into kilometres, you need to divide your measurement by 5 and multiply the answer by 8 (to convert from kilometres to miles, do the opposite – divide by 8 and then multiply by 5).

50 ÷ 5 = 10 × 8 = 80, so 50 miles per hour is the same as 80 kilometres per hour. 

Now you can work out the journey time. 120 ÷ 80 = 1.5, so the total time taken is 1.5 hours (or 1 hour and 30 minutes).

If you need to arrive in Ostend by 18:00, you need to set off 1 hour and 30 minutes before this time, which will be 16:30 (by the 24-hour clock). 

Final Answer: 16:30

Note – I have made a point of being thorough in this method to ensure you understand each point as we go. When you sit your QTS Skills Tests, your process will probably be much quicker as these techniques start to become second nature to you.

    Further Help

    If you require any further help with questions like this, we have created a selection of resources to provide all the help you need.

    Revision Book – The Guide to the QTS Skills Tests book devotes a whole chapter to each QTS numeracy topic, with detailed methods, worked examples and plenty of practice questions for you to have a go at. The book also includes three practice tests and fully worked solutions to every question.

    Practice Tests – Want more practice tests to see how ready you are? Take a look at our selection of practice papers for the QTS numeracy test (including some totally free papers as our gift to you).

    Revision Cheat Sheets – Our cheat sheets boil down everything you need to know to just the key points on the topic. They are a perfect resource for your last minute revision!