The conversion graph changes between kilometres and miles. (a) Use the graph to change \(60\) kilometres into miles. [1] (b) Use the graph to change \(30\) ...
Question 1 Report
The conversion graph changes between kilometres and miles.
(a) Use the graph to change \(60\) kilometres into miles. [1]
(b) Use the graph to change \(30\) miles into kilometres. [1]
(c) A car travels \(120\) kilometres. Calculate this distance in miles. [2]
Answer Details
The conversion graph is a straight line through the origin, so kilometres and miles are in direct proportion. Reading across the graph converts either way, and once the multiplier is known any distance can be converted by calculation.
(a) Read up from \( 60 \) on the kilometres axis to the line, then across to the miles axis.
\( 37.5 \) miles [B1]
(b) Now work in the opposite direction: start at \( 30 \) on the miles axis, read across to the line, then down to the kilometres axis.
\( 48 \) km [B1]
(c) \( 120 \) km is beyond the range of the graph, so use the multiplier instead of extending the line. From part (a), \( 1 \) km \( =\frac{37.5}{60}=0.625 \) miles.
\[ 120\times 0.625 \] [M1]
\[ =75 \text{ miles} \] [A1]
A check without the multiplier: \( 120 \) km is double \( 60 \) km, so it is double \( 37.5 \) miles, which is \( 75 \) miles. Miles are longer than kilometres, so the number of miles must always come out smaller than the number of kilometres.
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