A train covers a certain distance in 50 minutes at an average speed of 48 km/h. To reduce the total journey time to 40 minutes for the same distance, at what constant speed must the train run?

Introduction / Context:
Speed, distance, and time are related by distance = speed * time. For a fixed distance, if time decreases, speed must increase proportionally to keep distance constant.

Given Data / Assumptions:

• Initial speed v1 = 48 km/h; time t1 = 50 minutes = 5/6 h.
• Target time t2 = 40 minutes = 2/3 h.
• Distance remains the same.

Concept / Approach:
Compute the distance from the first leg, then divide by the new time to get the required speed.

Step-by-Step Solution:

Verification / Alternative check:
Proportion method: v2 / v1 = t1 / t2 = (50) / (40) = 1.25, hence v2 = 48 * 1.25 = 60 km/h.

Why Other Options Are Wrong:
All other speeds fail to achieve 40 km in 40 minutes.

Common Pitfalls:
Not converting minutes to hours; mixing up proportionality (speed inversely proportional to time for fixed distance).

Final Answer:
60 km/h