A’s speed is 1 3/8 times B’s speed (that is, 11/8 of B). In a race, A gives B a start of 300 m and they finish together. What should be the total race length (distance A runs) so both reach the winning post simultaneously?

Introduction / Context:
When a faster runner gives a head-start but still aims to finish together, the time equality relates the full distance for the faster to the reduced distance for the slower via their speed ratio.

Given Data / Assumptions:

• vA = (11/8) vB.
• B’s head-start = 300 m.
• Let race length (A’s distance) be L; B runs L − 300.

Concept / Approach:
Equal finish times: L / vA = (L − 300) / vB. Substitute vA and solve for L.

Step-by-Step Solution:

Verification / Alternative check:
Times become equal: A’s time = 1,100 / (11/8 vB) = 800 / vB; B’s time = 800 / vB.

Why Other Options Are Wrong:
Other lengths do not satisfy the derived equality.

Common Pitfalls:
Subtracting 300 from the faster runner’s distance, or inverting the 11/8 ratio.

Final Answer:
1,100 m