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?

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Solve this multiple-choice question and choose the correct option.

Accepted Answer

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: L / ((11/8) vB) = (L − 300)/vB ⇒ (8L/11) = L − 300.Multiply by 11: 8L = 11L − 3,300 ⇒ 3L = 3,300 ⇒ L = 1,100 m. 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

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?

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