Question

A lap around a motocross track is mile. How many laps do you need to complete to finish a 6-mile race?

Answer 1

For 6 miles you have 6 laps

Explanation:

Given that the length of 1 lap is 1 mile.

The word lap means going round all of the track once.

So using ratio in fraction form:

`("lap")/("distance")->("1 lap")/("1 mile")`

Multiply by 1 and you do not change the value. However, 1 comes in many forms.

`color(green)( [("1 lap")/("1 mile") color(red)(xx1)] " "=" "[("1 lap")/("1 mile")color(red)(xx6/6) ] )" "=" "("6 laps")/("6 miles")`

So for 6 miles you have 6 laps
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`color(blue)("Showing the link between the ratio method and the shortcut method")`

`color(brown)("Using and example - in detail")`
Suppose 1 lap was 3 miles long. How many laps would you need to do to travel 20 miles.

Starting off as we did before

`("lap")/("miles")->("1 lap")/("3 miles")`

`1/3=("laps")/20`

This is the different method bit.

This is the same as `1/3=1/20xx"laps"`

Multiply both sides by 20

`1/3xx20=1/20xx20xx"laps"`

`20/3=color(magenta)(20/20)xx"laps"`

`color(magenta)("but "20/20=1)`

`20/3=color(magenta)(1)xx"laps"`

laps count`=20/3 = 6 2/3`
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`color(brown)("This is how it should look when jumping steps")`

Let the count of laps be `x`

`("lap")/("distance")->1/3=x/20`

`1/3xx20=x`

`x=6 2/3`