A car covers four successive 6 km stretches at speeds of 25 kmph, 50 kmph, 75 kmph and 150 kmph respectively. Its average speed over this distance is
Answers
The average speed of the car is 50 km/hr.
• Given, a car travels a distance in four successive stretches of 6 km each, with varying speed. This means, every 6 km is travelled by the car at a different speed.
• For the first 6 km,
speed = 25 km/hr
=> Time (T1) = distance/speed = 6/25 hr
• For the second 6 km,
speed = 50 km/hr
=> Time (T2) = distance/speed = 6/50 hr
• For the third 6 km,
speed = 75 km/hr
=> Time (T3) = distance/speed = 6/75 hr
• For the fourth 6 km,
speed = 150 km/hr
=> Time (T4) = distance/speed = 6/150 hr
• Total distance travelled by the car = 6 km + 6 km + 6 km + 6 km =
24 km
Total time taken by the car to cover 24 km = T1 + T2 + T3 + T4 = 6/25 hrs + 6/50 hr + 6/75 hr + 6/150 hr
= {(6 × 6) + (6 × 3) + (6 × 2) + (6 × 1) } / 150 hr
= {(36 + 18 + 12 + 6) / 150 } hr
= 72/150 hr
= 12/25 hr
• Average speed = Total distance travelled / Total speed
=> Average speed of the car =
24 km / (12/25) hr = (24 × 25) / 12
= 50 km/hr