A student waiting at a stoplight notices that her turn signal, which has a period of \(0.85 \mathrm{~s}\), makes one blink exactly in sync with the turn signal of the car in front of her. The blinker of the car ahead then starts to get ahead, but \(17 \mathrm{~s}\) later the two are exactly in sync again. What is the period of the blinker of the other car?