Irodov 1.3: Accelerate, cruise, decelerate — find the cruise time

(Paraphrased.) A car starts from rest, speeds up uniformly with acceleration $w$, then moves at constant speed, and finally slows uniformly with the same magnitude $w$ to a stop. The total time is $\tau$ and the mean speed is $\langle v\rangle$. Find how long the car moved at constant speed.