Question

A train with a speed of 40 km/hr passes a cyclist coming it the opposite direction in 3 second. if the cyclist were to go in the same direction the train would have taken 2 seconds more to pass him . what is the speed of the cyclist?

Answer 1

If a train takes 2 second with the speed of 40 km/hr
then, the cyclist took 3 second with the speed of ?

2 : 40
3 : ?
cross multiple

3 × 40 / 2
120 / 2
60 km/hr
Hence, the cyclist's speed was 60 km/ hr.

Answer 2

Hey.

Let the speed of the cyclist be x m/s

Speed of train = 40 kmph = 40×5/18

= 100/9 m/s

When cyclist comes in opposite direction :

t = 3 s

relative speed / net speed = 100/9 + x m/s

When cyclist comes in same direction :

t = 3+2 = 5 s

relative or net speed = 100/9 - x m/s

Since the cyclist has to travel the same distance both the times i.e., the distance equivalent to the length of the train to cross the train

so, 3×(100/9 + x ) = 5×(100/9 - x ). km

so, 300/9 + 3x = 500/9 - 5x

or, 200/9 = 8x

or, x = 200/(9 × 8 ) = 200/72 m/s

or, x = 200/72 × (18/5) kmph

or, x = 10 kmph

Hence , the speed of the cyclist is 10 kmph.

Thanks.