Multiple choice

A courier vehicle travels three equal distance segments at uniform speeds of 20 km/h, 30 km/h, and 60 km/h respectively. What is the average speed of the vehicle for the entirety of its journey?

  1. 30 km/h

  2. 35 km/h

  3. 40 km/h

  4. 45 km/h

  5. None
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A Correct answer
Explanation

Average speed = Total distance / Total time. Let each segment be d. Total distance = 3d. Total time = d/20 + d/30 + d/60 = (3d + 2d + d) / 60 = 6d/60 = d/10. Average speed = 3d / (d/10) = 30 km/h.

AI explanation

For equal distance segments traveled at different uniform speeds, the average speed is found using the harmonic mean formula for three speeds: 3xyz divided by (xy + yz + zx). Substituting the speeds 20 km/h, 30 km/h, and 60 km/h gives a numerator of 3 multiplied by 36000, which is 108000. Dividing this by the denominator (600 + 1800 + 1200), which is 3600, gives an average speed of 30 km/h.

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