Question

A cyclist rides his bicycle with a speed of 30 m/s for the first half and the next half length he covers with a speed of 45 m/s . Find the average speed of the cyclist.

Answer 1

For the first half of the distance speed, V1=30m/s
For the second half of the distance speed,V2=45m/s
Average speed=(2V1V2)/V1+V2=[2(30)(45)]/30+45=2700/75=36m/s

Answer 2

answer : 36 m/s

explanation : A cyclist rides his bicycle with a speed 30 m/s for the first half and the next half length he covers with a speed of 45 m/s.

Let total distance travelled by cyclist is x.

half of distance covered with speed 30m/s.

so, time taken to cover half of distance x , t = (x/2)/30 = x/60 sec ...(1)

again, another half of distance covered with speed 45m/s.

so, time taken to cover another half of distance x, t = (x/2)/45 = x/90 sec....(2)

now, average speed = total distance/total time taken

= (x/2 + x/2)/(x/60 + x/90)

= x/x[1/60 + 1/90]

= 60 × 90/(60 + 90)

= 5400/150

= 36 m/s

hence, average speed of the cyclist is 36m/s

shortcut : average speed = 2v1v2/(v1 + v2)

given, v1 = 30 m/s and v2 = 45m/s

so, average speed = 2 × 30 × 45/(30 + 45)

= 2700/75

= 36 m/s