1. (7 points) Automobile traffic passes a point P on a road of width w feet with an average rate of R vehicles per second. Although the arrival of automobiles is irregular, traffic engineers have found that the average waiting time T until there is a gap in traffic of at least t seconds is approximately T = te Rt seconds. A pedestrian walking at a speed of 3.5 ft/s requires t = w/3.5 s to cross the road. Therefore, the average time the pedestrian will have to wait before crossing is f (w, R) = (w/3.5)eWR/3.5 s. (a) What is the pedestrian's average waiting time if w = 25 ft and R = 0.2 vehicle per second? (b) Use the Linear Approximation to estimate the increase in waiting time if w is increased to 27 ft. Answer: (a) ( 6 )