Discussion

A can give B a start of 20 metres and C a start of 39 metres in a walking race of 400 metres. How much can B give C a start?

Answer: A

In these problems the two players are compared by the scores they reach in the same time, so their rates are in the ratio of those scores.

\[ A\,400 : B\,380, \qquad A\,400 : C\,361 \]

\[ B : C = 380 : 361 = 20 : 19 \]

In a 400 m race, when B finishes:

\[ C = 400 \times \frac{19}{20} = 380 \text{ m} \]

\[ \text{B can give C} = 400 - 380 = 20 \text{ m} \]

The difference of the starts, \( 39 - 20 = 19 \), is close but not the answer, since C's deficit is now measured over B's 400 m rather than A's.

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