Numerical answer
In a 1 km race, A beats B by 100 m, and in another 1 km race B beats C by 100 m. By how many metres would A beat C in a 1 km race, if all run at their constant speeds?
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Answer: 190
When A runs 1000 m, B runs 900 m, so B's speed = 0.9 × A's.
When B runs 1000 m, C runs 900 m, so C's speed = 0.9 × B's = 0.81 × A's.
When A finishes 1000 m, C has run 810 m. A beats C by 190 m.
The answer 200 m (100 + 100) is wrong because B's 100 m lead over C is measured when B has run 1000 m, not 900 m. Speed ratios multiply.
When B runs 1000 m, C runs 900 m, so C's speed = 0.9 × B's = 0.81 × A's.
When A finishes 1000 m, C has run 810 m. A beats C by 190 m.
The answer 200 m (100 + 100) is wrong because B's 100 m lead over C is measured when B has run 1000 m, not 900 m. Speed ratios multiply.
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