A group of pilgrims planned to cover a total distance of 140 km in three…
2026
A group of pilgrims planned to cover a total distance of 140 km in three stages. They covered 104 km by train at a speed of 120 km/hr, and 24 km by bus at 40 km/hr. The rest of the journey is to be completed on foot. At what speed must they walk for the overall average speed for the entire journey to be exactly 50 km/hr?
Answer: D. 9 km/hr — Concept: For a journey made in stages, average speed is total distance divided by total time — it is never the plain average of the individual stage speeds.…
- A.
11 km/hr
- B.
24 km/hr
- C.
10 km/hr
- D.
9 km/hr
Attempted by 16 students.
Show answer & explanation
Correct answer: D
Concept: For a journey made in stages, average speed is total distance divided by total time — it is never the plain average of the individual stage speeds. So fixing a target average speed fixes the total time budget for the whole journey, and each stage consumes distance divided by that stage's speed out of that budget. The unknown stage speed is then whatever makes its leg fit the time that is left.
Application to this journey:
Walking leg = 140 - 104 - 24 = 12 km.
Total time allowed = 140 / 50 = 14/5 hr = 2 hr 48 min.
Train time = 104 / 120 = 13/15 hr.
Bus time = 24 / 40 = 3/5 hr = 9/15 hr.
Time already used = 13/15 + 9/15 = 22/15 hr.
Time left for the walk = 14/5 - 22/15 = 42/15 - 22/15 = 20/15 = 4/3 hr = 1 hr 20 min.
Required walking speed = 12 / (4/3) = 12 x 3/4 = 9 km/hr.
Cross-check: the three stage times are 13/15 + 9/15 + 20/15 = 42/15 = 2.8 hr for 140 km, and 140 / 2.8 = 50 km/hr exactly, as required. Contrast this with the plain average of the three speeds, (120 + 40 + 9) / 3 = 56.33 km/hr, which is not 50 - confirming that stage speeds must never be averaged directly.