Discussion

A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?

Answer: A

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.

\[ A\,1000 : B\,900, \qquad A\,1000 : C\,800 \]

\[ B : C = 900 : 800 = 9 : 8 \]

In a 1000 m race, when B finishes:

\[ C = 1000 \times \frac{8}{9} = 888.88 \text{ m} \]

\[ \text{B can give C} = 1000 - 888.88 = 111.12 \text{ m} \]

The two starts do not subtract to 100 m; B's advantage is measured over a shorter run than A's was.

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