By how many metres does A beat C in a 1,000 m…

By how many metres does A beat C in a 1,000 m race between them?

Question 23

MediumOriginal question

In a 1,000 m race A beats B by 100 m, and in another 1,000 m race B beats C by 50 m. The runners keep the same speeds in every race.

By how many metres does A beat C in a 1,000 m race between them?

140 mCorrect answerYour answer144 mCorrect answerYour answer145 mCorrect answerYour answer150 mCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

When A runs 1,000 m, B runs 900 m; C runs $\frac{950}{1{,}000}$ of B's distance: $900 \times 0.95 = 855$ m.
A wins by $1{,}000 - 855 = 145$ m.

Worth noting

150 m adds the two margins, but B runs only 900 m in A's race, so B's lead over C shrinks to 45 m.

Ten questions from Races & Games, at your own pace.

Ten questions from Races & Games, at your own pace.