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?

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:

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.