Automobile traffic passes a point P on a road of width w feet with an average rate of R vehicles per second. Althoughthe arrival of automobiles is irregular, traffic engineers have found that the average waiting time T' until there is a gap intraffic of at least t seconds is approximately T = teRi seconds. A pedestrian walking at a speed of 3.1 ft/s requires1 = s to cross the road. Therefore, the average time the pedestrian will have to wait before crossing isS(w, R) = () e R/3.1 §.What is the pedestrian's average waiting time if w = 24 ft and R = 0.2 vehicle per second?(Use decimal notation. Give your answer to two decimal places.)t =Use the Linear Approximation to estimate the increase in waiting time if w is increased to 26 ft.(Use decimal notation. Give your answer to two decimal places.)Af =Estimate the waiting time if the width is increased to 26 ft and R decreases to 0.19. Af =Estimate the waiting time if the width is increased to 26 ft and R decreases to 0.19.(Use decimal notation. Give your answer to two decimal places.)=What is the rate of increase A in waiting time per 1-ft increase in width when w = 33 ft andR = 0.5 vehicle per second?(Use decimal notation. Give your answer to two decimal places.)A =

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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 1 seconds is approximately T = teRt seconds. A pedestrian walking at a speed of 3.1 ft/s requires 1 = s to cross the road. Therefore, the average time the pedestrian will have to wait before crossing is S(w, R) = () RI.1 §. What is the pedestrian's average waiting time if w = 24 ft and R = 0.2 vehicle per second? (Use decimal notation. Give your answer to two decimal places.)

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 1 seconds is approximately T = teRt seconds. A pedestrian walking at a speed of 3.1 ft/s requires 1 = s to cross the road. Therefore, the average time the pedestrian will have to wait before crossing is S(w, R) = () RI.1 §. What is the pedestrian's average waiting time if w = 24 ft and R = 0.2 vehicle per second? (Use decimal notation. Give your answer to two decimal places.)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

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 = teRi seconds. A pedestrian walking at a speed of 3.1 ft/s requires
1 = s to cross the road. Therefore, the average time the pedestrian will have to wait before crossing is
S(w, R) = () e R/3.1 §.
What is the pedestrian's average waiting time if w = 24 ft and R = 0.2 vehicle per second?
(Use decimal notation. Give your answer to two decimal places.)
t =
Use the Linear Approximation to estimate the increase in waiting time if w is increased to 26 ft.
(Use decimal notation. Give your answer to two decimal places.)
Af =
Estimate the waiting time if the width is increased to 26 ft and R decreases to 0.19.

Af =
Estimate the waiting time if the width is increased to 26 ft and R decreases to 0.19.
(Use decimal notation. Give your answer to two decimal places.)
=
What is the rate of increase A in waiting time per 1-ft increase in width when w = 33 ft and
R = 0.5 vehicle per second?
(Use decimal notation. Give your answer to two decimal places.)
A =

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