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April 11th, 2018, 12:43 AM   #1
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This question seems simple but....

Alfie, Ben and Charlie are brothers. In a 100m race, Alfie beats Ben by 15m; in a second 100m race, Ben beats Charlie by 20m. Assuming each boy runs each of his races at the same constant speed, by how many metres would Alfie beat Charlie in a 100m race?

(In a race, X, beats Y by n metres if Y is n metres behind when X crosses the finish line.)

Last edited by skipjack; April 11th, 2018 at 03:14 AM.
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April 11th, 2018, 03:26 AM   #2
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In every race, let's assume that the brothers start at the same time and have the same distance to run.

While Ben runs 100m, Charlie runs only 80m.

For running at constant speed, the above implies that while Ben runs 85m, Charlie would run 85m × 80/100 = 68m. It follows that Alfie would beat Charlie by 100m - 68m = 32m in a 100m race (run at the same speeds).
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