# Who will win?

Two cars $$A$$ and $$B$$ are racing along a straight line, car $$A$$ is leading and their relative velocity is directly proportional to the distance between the two cars. When the lead of car $$A$$ is $$x_{1}=10\text{ m}$$, it is running $$10\text{ ms}^{-1}$$ faster than car $$B$$. If the time taken by car $$A$$ to increase its lead to $$x_{2}=20\text{ m}$$ from car $$B$$ is in the form $$t=\ln n$$, find $$n$$.

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