Question

A bus covers a distance of first 50 km in 40 minutes, next 50 km at a speed of 2 km per minute and the next 30 km at a speed of 1.0 km per minute. What is its average speed during the entire journey?

• A. 81.2 kmph
• B. 64.8 kmph
• C. 80.8 kmph
• D. 84.1 kmph
• E. 82.1 kmph

Hint:

Average speed = Total distance / Total time; do not average the speeds directly.

Answer 1

Answer: (E)

Step 1: Calculating Time for Each Segment:
Segment 1: Distance = 50 km, Time = 40 minutes = \(\frac{40}{60} = \frac{2}{3}\) hours.
Segment 2: Distance = 50 km, Speed = 2 km/min = \(2 \times 60 = 120\) kmph.
Time = \(\frac{50}{120} = \frac{5}{12}\) hours.
Segment 3: Distance = 30 km, Speed = 1 km/min = 60 kmph.
Time = \(\frac{30}{60} = \frac{1}{2}\) hours.

Step 2: Total Distance and Total Time:
Total Distance = \(50 + 50 + 30 = 130\) km.
Total Time = \(\frac{2}{3} + \frac{5}{12} + \frac{1}{2} = \frac{8}{12} + \frac{5}{12} + \frac{6}{12} = \frac{19}{12}\) hours.

Step 3: Average Speed:
Average Speed = \(\frac{\text{Total Distance}}{\text{Total Time}} = \frac{130}{19/12} = 130 \times \frac{12}{19} = \frac{1560}{19} \approx 82.105\) kmph ≈ 82.1 kmph.