A bus travels 1/3 of the distance initially at a speed of 40 km/h, the next 1/3 of the distance at 50 km/h, and the final 1/3 of the distance at 60 km/h. Find the average speed of the bus for the entire journey. (Round off your answer to two decimal places.)

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Accepted Answer

Let the total distance be D km. Each segment is D/3 km.

Time for first segment = (D/3) / 40 = D/120 hours
Time for second segment = (D/3) / 50 = D/150 hours
Time for third segment = (D/3) / 60 = D/180 hours

Total time taken = D/120 + D/150 + D/180
To add, take LCM of denominators (120, 150, 180):
LCM = 1800

D/120 = 15D/1800
D/150 = 12D/1800
D/180 = 10D/1800

Total time = (15D + 12D + 10D)/1800 = 37D/1800 hours

Average speed = Total distance / Total time = D / (37D/1800) = 1800/37 km/h

1800/37 ≈ 48.6486 km/h ≈ 48.65 km/h (rounded to two decimal places)

Therefore, the average speed is 48.65 km/h.

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