Discussion

In a race of 200 m, A can beat B by 31 m and C by 18 m. In a race of 350 m, C will beat B by :

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.

\[ A\,200 : B\,169, \qquad A\,200 : C\,182 \]

\[ C : B = 182 : 169 \]

In a 350 m race, when C finishes:

\[ B = 350 \times \frac{169}{182} = 325 \text{ m} \]

\[ \text{C beats B by } 350 - 325 = 25 \text{ m} \]

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