Problem 2 - A very long walk?
Problem 2 is all about measuring lengths and distances…which might seem very long or very short depending on what units you use.
Maths teacher Chris Smith is here to help you get the measure of things.
The Maths Week Scotland Daily Challenges have been set by the Scottish Mathematical Council.
Chris Smith: Most of the time we measure things using the Metric system – centimetres, metres, kilometres.
Before the Metric system we measured lengths in the Imperial System. It was a lot more complicated.
We still use some of the old Imperial units– like miles for instance.
But there were lots more length units. Here’s how some of them are connected.
There are 12 inches in a foot
And 3 feet in a yard.
22 yards make a chain.
There are 10 chains in a furlong.
And finally 8 furlongs make a mile.
It’s a good idea to take a note of that conversion chart.
One day, intrepid Annie walks a distance of 316,800 inches. Sounds like a very long walk. But is it really?
How far is that in miles?
Think about how you would solve this problem if it was in metric measurements. How would you convert from millimetres or centimetres to kilometres? Can you use the same method but with different numbers?
This question would be a lot easier if you used a calculator.
But let’s see if you can do it without. You’ll need to refer to our Imperial Conversion Chart.
Here's the problem:
One day, intrepid Annie walked a distance of 316,800 inches. How far is that in miles?
We're using the Imperial System of measurement here, so use this table to help you.
| 12 inches | = 1 foot |
| 3 feet | = 1 yard |
| 22 yards | = 1 chain |
| 10 chains | = 1 furlong |
| 8 furlongs | = 1 mile |
Need a hint?
Think about how you would solve this problem if it was in metric measurements.
How would you convert from millimetres or centimetres to kilometres?Can you use the same method but with different numbers?
This question would be a lot easier if you used a calculator but if you like a challenge see if you can do it without.
Solution
Chris Smith: How did you get on?
Did you manage to get the answer without a calculator?
This problem is all about dividing, dividing and dividing again. Let’s take a look.
Annie walks 316,800 inches.We’ll convert that into miles using all our other Imperial units along the way, by dividing.
There are twelve inches in a foot, so first divide 316,800 by 12 to turn inches into feet.26, 400 feet.
Then divide 26, 400 feet by 3 to make feet into yards.Which is 8, 800 yards.
Next divide 8,800 by 22 to turn yards into chains. Which gives us 400 chains. There are ten chains in a furlong so divide 400 by 10 to get 40 furlongs.
And finally, divide the number of furlongs by 8 to give the answer in miles. 40 divided by 8 is five.
So the answer is Annie walked 5 miles!
This problem is all about dividing, dividing and dividing again.
Annie walks 316,000 inches. To work out how far this is in miles, we need to work through all the other Imperial units.
We're converting from a large number of small units to a small number of large units. That means we need to divide each time.
There are 12 inches in 1 foot, so first divide 316,000 by 12 to turn inches into feet.
316,000 ÷ 12 = 26,400
Annie walked 26,400 feet.
Next we need to convert feet into yards.
There a 12 feet in 1 yard so divide 26,400 feet by 3 to make feet into yards.
26,400 ÷ 3 = 8,800
Annie walked 8,800 yards.
There are 22 yards in 1 chain. So divide 8,800 by 22 to turn yards into chains.
8,800 ÷ 22 = 400
So Annie walked 400 chains.
There are 10 chains in 1 furlong so divide 400 by 10 to turn chains into furlongs.
400 ÷ 10 = 40
Annie walked 40 furlongs.
Finally, we need to convert from furlongs to miles.
There are 8 furlongs in 1 mile so divide 40 by 8 to give the answer in miles.
40 ÷ 8 = 5
So the answer is Annie walked 5 miles!
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