Express vs local with periodic stops — distance covered by the local: An express runs at 100 km/h between stops and halts 3 min after every 75 km. A local runs at 50 km/h between stops and halts 1 min after every 25 km. If they start together and, in the time the express covers 600 km, how many kilometres does the local cover (including its own stops)?

Introduction / Context:
When trains have cruising speeds and scheduled halts, the end-to-end time combines motion time and halt time. Here we compute the express’s total time for 600 km, then determine the local’s distance within the same duration.

Given Data / Assumptions:

• Express: 100 km/h (cruise), halt 3 min after each 75 km segment.
• Local: 50 km/h (cruise), halt 1 min after each 25 km segment.
• No halt is counted at the final destination instant.

Concept / Approach:
Express motion time = 600/100 = 6 h. Number of halts during the run = 600/75 − 1 = 8 − 1 = 7 halts ⇒ 21 min. Total express time = 6 h 21 min = 381 min. In blocks, the local spends 30 min moving per 25 km plus 1 min halt = 31 min per full 25 km block.

Step-by-Step Solution:

Verification / Alternative check:
If a stop were counted at the terminal, total express time would be 384 min, yielding 310 km for the local, which is not among the original best options—so excluding a terminal halt is consistent.

Why Other Options Are Wrong:
400, 405, 415.5 km assume higher effective average or miscount halts; 307.25 km is a rounding artifact not supported by whole-block accounting.

Common Pitfalls:
Counting a destination halt, or forgetting that the local’s final partial segment involves no halt unless a 25 km boundary is reached.

Final Answer:
307.5 km