A student waiting at a stoplight notices that her turn signal, which has a period of 0.85 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 s later the two are exactly in sync again. What is the period of the blinker of the other car?

The answer to the question is

The period of the blinker of the other car = 0.809 s

Explanation:

To solve this we list out the variables thus

Period of the student turn signal = 0.85 s, Period of the other car signal = T

In 17 seconds the two cars signal are in sync again

Therefore the frequency of the students car signal = 1/0.85 = 1.176 Hz and the frequency of the other car signal is 1/T however is 17 seconds the other car is ahead by one cycle thus

Therefore

17/T - 17/0.85 = 1

Which gives 17/T = 1 + 17/0.85 = 17.85/0.85 =

Multiplying both sides by T we have

17 = T*17.85/0.85

Therefore T = 17*0.85/17.85 = 0.809 s

The period of the blinker of the other car is 0.809 s