Multiple choice

A motorcyclist covered two-thirds of a total journey at his usual speed. He covered the remaining distance at three-fourth of his usual speed. As a result he arrived 30 min later than the time he would have taken at usual speed. If the total journey was 180 km, then what is his usual speed?

  1. 40 km/h

  2. 36 km/h

  3. 30 km/h

  4. 32 km/h
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A Correct answer
Explanation

Let usual speed = v. Distance = 180 km. Time at usual speed = 180/v hours. Actual time: (120/v) + (60/(3v/4)) = 120/v + 80/v = 200/v hours. Delay = 200/v - 180/v = 20/v hours = 30 minutes. So 20/v = 0.5, giving v = 40 km/h.

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