Automobile traffic passes a point P on a road of width w feet at anaverage rate of R vehicles per second. Although the arrival of automobilesis irregular, traffic engineers have found that the average waiting time Tuntil there is a gap in traffic of at least t seconds is approximately T = t eRtseconds. A pedestrian walking at a speed of 3.5 ft/s (5.1 miles per hour) 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 timeif w is increased to 27 ft.( c) Estimate the waiting time if the width is increased to 27 ft and R decreases to 0.18.( d) What is the rate of increase in waiting time per 1-ft increase in widthwhen w = 30 ft and R = 0.3 vehicle per second?
Automobile traffic passes a point P on a road of width w feet at 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 = t eRt
seconds. A pedestrian walking at a speed of 3.5 ft/s (5.1 miles per hour) 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.
( c) Estimate the waiting time if the width is increased to 27 ft and R decreases to 0.18.
( d) What is the rate of increase in waiting time per 1-ft increase in width
when w = 30 ft and R = 0.3 vehicle per second?
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