How long should a traffic light stay yellow before turning red? One study suggests that for a car approaching a 40 ft wide intersection under normal driving conditions, the length of time, y, that a light should stay yellow, in seconds, is given by the equation y = 1 + v/25+ 50/v, where v is the velocity of an approaching car in feet per second.
a. Rewrite the equation in rational function form.
b. Enter the original equation as Y1 and your simplified equation as Y2 into your calculator. Check using the table feature that the values of both functions are the same. What does this tell you?
c. If the speed limit at a particular intersection is 45 mi/h, how long should the light stay yellow?
d. If cars typically travel at speeds ranging from 25 mi/h to 55 mi/h at that intersection, what is the possible range of times that a light should stay yellow?