Linked handicaps with time gap: A gives B 40 m and C 82 m in an 880 m race. Also, B finishes 9 s before C over the same 880 m. How long (in minutes) does C take to run 880 m?

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

Accepted Answer

Introduction / Context:This is a chained comparison problem: two distance advantages relate A–B and A–C speeds; a time gap relates B–C directly. We solve for C’s time using speed ratios and the given 9 s difference. Given Data / Assumptions: Over 880 m: A vs B → B is at 840 m when A finishes. Over 880 m: A vs C → C is at 798 m when A finishes. B beats C by 9 s over 880 m. Concept / Approach:vA/vB = 880/840 = 22/21 and vA/vC = 880/798 = 440/399. Hence vB/vC = (vA/vC)/(vA/vB) = (440/399)/(22/21) = 140/133. Use the 9 s difference to find absolute times. Step-by-Step Solution: Let vB be unknown. Then vC = vB * (133/140).tB = 880 / vB; tC = 880 / vC = 880 / (vB * 133/140) = 880 * 140 / (133 vB).tC - tB = 9 ⇒ 880 * 140/(133 vB) - 880/vB = 9.Simplify: 880 * (140/133 - 1) / vB = 9 ⇒ 880 * (7/133) / vB = 9 ⇒ vB = 880 * 7 / (133 * 9).Then tC = 880 / vC = 180 s = 3 min. Verification / Alternative check:Plugging back shows B's time is 171 s and C's time 180 s, confirming the 9 s gap. Why Other Options Are Wrong:3.25/4 minutes contradict the achieved 9 s gap with the derived ratios. Common Pitfalls:Directly treating distance gaps as time gaps; you must use speed ratios first, then time difference. Final Answer:3 min.

Linked handicaps with time gap: A gives B 40 m and C 82 m in an 880 m race. Also, B finishes 9 s before C over the same 880 m. How long (in minutes) does C take to run 880 m?

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