Multiple choice

A person covers 50% of the journey at 28 km/h, 25% at 42 km/h, and the remainder at 14 km/h. What is his average speed?

  1. 24 km/h

  2. 21 km/h

  3. 28 km/h

  4. 30 km/h
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let total distance be 400 km. 50% (200 km) at 28 km/h takes 200/28 = 50/7 hours. 25% (100 km) at 42 km/h takes 100/42 = 50/21 hours. 25% (100 km) at 14 km/h takes 100/14 = 50/7 hours. Total time = 50/7 + 50/21 + 50/7 = (150+50+150)/21 = 350/21 = 50/3 hours. Average speed = 400 / (50/3) = 400 * 3 / 50 = 24 km/h.

AI explanation

Using the average speed formula for equal distances traveled at different speeds, we find the harmonic mean since the percentages represent equal distance fractions. Assuming a total distance of 84 km for simple arithmetic, the times taken for the three parts are 1.5 hours, 0.5 hours, and 1.5 hours. The total time for the journey is 3.5 hours, so the average speed is 84 divided by 3.5, which equals 24 km/h.

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