Discussion

In a 100 m race, A can give B 10 m and C 28 m. In the same race B can give C:

Answer: B

In these problems the two runners are compared by the distances they cover in the same time, so their speeds are in the ratio of those distances.

\[ A\,100 : B\,90, \qquad A\,100 : C\,72 \]

\[ B : C = 90 : 72 \]

In a 100 m race, when B finishes:

\[ C = 100 \times \frac{72}{90} = 80 \text{ m} \]

\[ \text{B can give C} = 100 - 80 = 20 \text{ m} \]

The difference of the two handicaps, \( 28 - 10 = 18 \), is not the answer, because B's lead is measured over a shorter effective distance.

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