Two runners have a race. The first runner decides to run with his full speed \(v_1=9~\mbox{m/s}\) over the 250 meters of the race and then slows to \(v_2=7~\mbox{m/s}\) for the rest, since he's tired. The second runner wants to save energy, so he runs with \(v_3=8~\mbox{m/s}\) for the whole time. If the distance of the race is \(L=500~\mbox{m}\), by what time **in seconds** does the second runner beat the first?

Moral of the story: slightly slower but steadier wins the race.

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