Multiple choice

Emma, a delivery driver for a local courier service, has a multi-stop route to complete. She drives her delivery van at an average speed of 40 kmph for 30% of the total distance while navigating city traffic, at 60 kmph for 40% of the total distance on highways, at 50 kmph for 20% of the total distance through suburban areas, and at 30 kmph for the remaining 10% of the total distance on rural roads. What is Emma's average speed for the entire journey?

  1. 42.61 kmph

  2. 46.51 kmph

  3. 54.15 kmph

  4. 61.54 kmph
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Average speed = Total Distance / Total Time. Let total distance be D. Time = (0.3D/40) + (0.4D/60) + (0.2D/50) + (0.1D/30) = D * (0.0075 + 0.00666 + 0.004 + 0.00333) = D * 0.0215. Average speed = D / (0.0215D) = 46.51 kmph.

AI explanation

Using the harmonic mean formula for average speed when distances are equal, we calculate the total distance as a fraction (0.3 + 0.4 + 0.2 + 0.1 = 1). The average speed equals total distance divided by total time, giving 1 divided by the sum of each distance fraction divided by its speed: (0.3/40) + (0.4/60) + (0.2/50) + (0.1/30). This yields 1 divided by 0.0215, resulting in 46.51 kmph.

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