In a 1 km race, A beats B by 80 m (i.e., B covers 920 m when A covers 1,000 m), and B beats C by 60 m (i.e., C covers 940 m when B covers 1,000 m). By how many meters does A beat C in the same 1 km race?

Question

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

Curioustab · Accepted Answer

Introduction / Context:Use chained speed ratios to compare two runners not racing directly. Once vA/vC is known, compute C’s distance at the instant A completes 1,000 m and subtract from 1,000 m to obtain the margin. Given Data / Assumptions: vA/vB = 1000/920 = 25/23. vB/vC = 1000/940 = 50/47. Concept / Approach:vA/vC = (25/23)*(50/47) = 1250/1081. When A finishes 1,000 m, C has covered 1,000 * 1081/1250 = 864.8 m. Step-by-Step Solution: Margin = 1,000 − 864.8 = 135.2 m. Verification / Alternative check:Proportional-time check matches the computed distance for C. Why Other Options Are Wrong:Other values do not match the compounded ratio 1250/1081. Common Pitfalls:Adding meter advantages directly; this is invalid across different base races. Final Answer:135.2 m

In a 1 km race, A beats B by 80 m (i.e., B covers 920 m when A covers 1,000 m), and B beats C by 60 m (i.e., C covers 940 m when B covers 1,000 m). By how many meters does A beat C in the same 1 km race?

Answer

Explanation