A runs at 1 2/3 (that is, 5/3) times the speed of B. If A gives B a start of 40 m and they finish together, how far from A’s starting line should the winning post be placed?

Introduction / Context:
Starts (head-starts) in races shift the effective distance each runner must cover. If two runners finish together, the time taken by both is equal. With a start advantage to the slower runner, we relate distances to speeds using the time equality for the same finishing instant.

Given Data / Assumptions:

• A’s speed : B’s speed = 5 : 3.
• Head-start to B = 40 m.
• Let race length (distance A runs) be D.

Concept / Approach:
Time = distance / speed. With equal finish time: D / vA = (D − 40) / vB. Substitute vA / vB = 5/3 to solve for D.

Step-by-Step Solution:

Verification / Alternative check:
Times: A takes 100 / (5k) = 20/k; B takes 60 / (3k) = 20/k. Equal ⇒ consistent.

Why Other Options Are Wrong:
75, 125, or 200 m do not satisfy the equality when substituted.

Common Pitfalls:
Interpreting “start” as extra distance for A instead of reduced distance for B, or inverting the given speed ratio.

Final Answer:
100 m