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Solution for distance

In a race over a distance s, runner A starts from rest and accelerates at a1 for the first distance x and then runs at constant speed. Runner B starts from rest and accelerates at a2 for the first distance x and then runs at constant speed. Runner A begins running as soon as the race begins but B first takes a nap to rest up.

What is the longest nap that B can take and still not lose the race?

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