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Everyday maths 1
Everyday maths 1

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2.1 Adding distances

Many trips have more than one stop. To calculate how far you have to travel you need to add together the distances between stops.

Example: The sales trip

A sales rep has to travel from Edinburgh to York, then to London, and then back to Edinburgh. How far will they travel?

Method

Use the mileage chart to find the distances between Edinburgh and York, York and London, and London and Edinburgh.

The distance between Edinburgh and York is 186 miles.

Described image
Figure 14 Edinburgh to York on a mileage chart
Show description|Hide description

A mileage chart showing the distances between Edinburgh, Birmingham, Cardiff, Dover, Leeds, Liverpool, London, Manchester, Newcastle and York. The distance between Edinburgh and York is highlighted (186 miles).

Figure 14 Edinburgh to York on a mileage chart

London to York is 194 miles.

Described image
Figure 15 London to York on a mileage chart
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A mileage chart showing the distances between Edinburgh, Birmingham, Cardiff, Dover, Leeds, Liverpool, London, Manchester, Newcastle and York. The distance between London and York is highlighted (194 miles).

Figure 15 London to York on a mileage chart

Returning from London to Edinburgh is 412 miles.

Described image
Figure 16 London to Edinburgh on a mileage chart
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A mileage chart showing the distances between Edinburgh, Birmingham, Cardiff, Dover, Leeds, Liverpool, London, Manchester, Newcastle and York. The distance between Edinburgh and London is highlighted (412 miles).

Figure 16 London to Edinburgh on a mileage chart

The total distance of the trip is:

  • 186 + 194 + 412 = 792 miles

Use the mileage table to help you with the following activity. Remember to check your answers once you have completed the questions.

Activity 5: Travelling across the UK

  1. You use a hire car to go from London to Cardiff, from Cardiff to Liverpool and then back to London. You pay 10p for each mile you drive.
    • a.How many miles must you pay for?
    • b.How much would this cost?
  1. You live in Newcastle and you want to buy a second-hand car trailer. There is one for sale in Leeds and one in York. Which one is closest?

Answer

  1. The answers are as follows:
    • a. You need to look up all the distances and then add them together:

      London to Cardiff is 150 miles.

      Described image
      Figure 17 London to Cardiff on a mileage chart
      Show description|Hide description

      A mileage chart showing the distances between Edinburgh, Birmingham, Cardiff, Dover, Leeds, Liverpool, London, Manchester, Newcastle and York. The distance between Cardiff and London is highlighted (150 miles).

      Figure 17 London to Cardiff on a mileage chart

      Cardiff to Liverpool is 165 miles.

      Described image
      Figure 18 Cardiff to Liverpool on a mileage chart
      Show description|Hide description

      A mileage chart showing the distances between Edinburgh, Birmingham, Cardiff, Dover, Leeds, Liverpool, London, Manchester, Newcastle and York. The distance between Cardiff and Liverpool is highlighted (165 miles).

      Figure 18 Cardiff to Liverpool on a mileage chart

      Liverpool to London is 198 miles.

      Described image
      Figure 19 Liverpool to London on a mileage chart
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      A mileage chart showing the distances between Edinburgh, Birmingham, Cardiff, Dover, Leeds, Liverpool, London, Manchester, Newcastle and York. The distance between Liverpool and London is highlighted (198 miles).

      Figure 19 Liverpool to London on a mileage chart

      So the total distance is:

  •  

    • 150 + 165 + 198 = 513 miles

  •  

    • b.The total distance is 513 miles and you pay 10p for each mile you drive. So you would pay:

  •  

    • 513 × 10 = 5,130p

  •  

    • You would not usually express an amount of money in this way, so let’s divide this total by 100 to find the amount in pounds:

  •  

    • 5,130 ÷ 100 = £51.30
  1. You need to use the mileage chart to compare the distances from Newcastle to Leeds and Newcastle to York.

    Newcastle to Leeds is 94 miles.

    Described image
    Figure 20 Newcastle to Leeds on a mileage chart
    Show description|Hide description

    A mileage chart showing the distances between Edinburgh, Birmingham, Cardiff, Dover, Leeds, Liverpool, London, Manchester, Newcastle and York. The distance between Leeds and Newcastle is highlighted (94 miles).

    Figure 20 Newcastle to Leeds on a mileage chart

    Newcastle to York is 82 miles.

    Described image
    Figure 21 Newcastle to York on a mileage chart
    Show description|Hide description

    A mileage chart showing the distances between Edinburgh, Birmingham, Cardiff, Dover, Leeds, Liverpool, London, Manchester, Newcastle and York. The distance between Newcastle and York is highlighted (82 miles).

    Figure 21 Newcastle to York on a mileage chart

    So the trailer in York is closer.

Summary

You have now completed the activities on using distance charts. This will help you with everyday life when you are planning a journey and or claiming mileage when travelling for work.