Start vs catch calculation: Two boys A and B run at 4.5 km/h and 6 km/h, respectively. Over a 1 km course, A has a 190 m start. By how many metres does B still win?

Introduction / Context:
With different speeds and a head-start, compute where the faster runner is when the slower finishes. The difference to the finish line is the winning margin.

Given Data / Assumptions:

• Course = 1000 m; A starts 190 m ahead → A needs 810 m.
• vA = 4.5 km/h; vB = 6 km/h; constant speeds.

Concept / Approach:
Time for A to finish tA = distance / speed. In that time, B covers vB * tA. Compare B’s covered distance with 1000 m.

Step-by-Step Solution:

Verification / Alternative check:
Ratio method: In A's finish time, B covers (vB/vA) * 810 = (6/4.5) * 810 = (4/3)*810 = 1080 → margin 80 m.

Why Other Options Are Wrong:
60/65/45/75 do not match the computed 80 m margin.

Common Pitfalls:
Subtracting the 190 m head-start from 1000 m directly without applying speed difference.

Final Answer:
80 m