Question
 In a 400 m race, A can beat B by 40 m, and B can beat
C by 40 m. By how many metres can A beat C in the same race? Assume all run at constant speeds.Solution
When A runs 400 m, B runs 400 − 40 = 360 m. ⇒ Speed ratio B : A = 360 : 400 = 9 : 10. When B runs 400 m, C runs 400 − 40 = 360 m. ⇒ Speed ratio C : B = 360 : 400 = 9 : 10. Thus, C : A = (C : B) × (B : A) = (9/10) × (9/10) = 81/100. So, when A runs 400 m, C runs (81/100) × 400 = 324 m. Difference = 400 − 324 = 76 m. Answer: A can beat C by 76 metres.
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