Question

The grid shows the travel graph for a train travelling from Audley to Cawley, stopping at Brookland.
Between which two towns is the train journey fastest ?
Give a reason for your answer.

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Hard

Solution

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1) Consider first part of the journey i.e. Audley to Brookland.
Distance between two stations is

Train left Audley at and reached Brookland at
Thus, time taken by train to reach from Audley to Brookland is

Thus, average speed of the train between these two stations is given by,

     (1)

2) Consider second part of the journey i.e. Brookland to Cawley.
Distance covered by train between these two stations is

Train left Brookland at and reached Cawley at
Thus, time taken by train to reach from Brookland to Cawley is

Thus, average speed of the train between these two stations is given by,


Now, we have to compare two fractions i.e. and

LCM of and is



The train journey was fastest between Brookland and Cawley.

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