Correct Answer - Option 2 : 37.5 km/hr
Given:
Speed when travelling (1/3)rd of the distance = 25 km/hr
Speed for remaining distance = 50 km/hr
Formula used:
Time = distance/speed
Average speed = total distance/total time
Calculation:
Let total distance travel be D.
1/3 rd of distance = D/3
And remaining distance = [D - (D/3)]
⇒ 2D/3
Time is taken while travelling (1/3)rd of the distance = [(D/3)/25] hours
Time is taken while travelling remaining of the distance = [(2D/3)/50] hours
Then, Average speed = [(D/3) + (2D/3)]/[{(D/3)/25} + {(2D/3)/50}]
⇒ Average speed = [(D/3) + (2D/3)]/[(D/75) + (D/75)]
⇒ Average speed = [(D + 2D)/3]/[2D/75]
⇒ Average speed = (3D × 75)/(2D × 3)
⇒ Average speed = 75/2
⇒ Average speed = 37.5 km/hr
∴ The average speed of the entire journey is 37.5 km/hr.