Question

A train travels between two stations A and B. While going from A to B, its average speed is 60 km/h, and when coming back from B to A, its average speed is 90 km/h. Find the average speed of the train during the whole journey. [4 MARKS]

Answer 1

Concept: 2 Marks
Application: 2 Marks

Let the distance AB = x km

Average speed while going from A to B = 60 km/h

Average speed while coming back from B to A = 90 km/h

Time taken to cover x km from A to B
$=\left(\frac{x}{60}\right)$ hours

Time taken to cover x km from B to A
$=\left(\frac{x}{90}\right)$ hours

Total time taken to cover 2x km
$=(\frac{x}{60}+\frac{x}{90})hours=\frac{x}{36}h$

Average speed during the whole journey
$=\frac{distance}{time}=\frac{2x}{\left(\frac{x}{36}\right)}km/h=72km/h$

Hence, the average speed of the train during the whole journey is 72 km/h.