Rahim travels a certain distance in 14 hours 40 minutes. He covers half the distance by train at 60 km/h and the other half by road at 50 km/h. What is the total distance traveled (in km)?

Introduction / Context:Splitting a journey into equal halves by distance but different speeds requires summing the two leg times and equating to the given total time to solve for the half-distance.

Given Data / Assumptions:

• Total time T = 14 h 40 min = 14.666... h.
• First half at 60 km/h, second half at 50 km/h.
• Let half-distance be x km.

Concept / Approach:Total time = x/60 + x/50. Solve for x, then total distance = 2x.

Step-by-Step Solution:

Verification / Alternative check:Time check: 400/60 = 6.666... h; 400/50 = 8 h; sum = 14.666... h as given.

Why Other Options Are Wrong:They result from arithmetic slips or misinterpreting “half the distance” vs. “half the time.”

Common Pitfalls:Confusing equal halves by distance with equal halves by time; forgetting to convert minutes to fractional hours.

Final Answer:800 km