Chapter 5.6, Problem 8E

Change in London Travel Time This exercise is a continuation of example 5.18. The rate of change $t^{\prime }$ in time to travel 1 mile with respect to traffic flow is the additional travel time that will be required if one additional vehicle is added to the flow. The formula for $t^{\prime }$ is

$t^{\prime }=\frac{48}{{\left(280-0.08q\right)}^2}$.

In parts a and b, do not round your answer.

a. If the traffic flow is 1000 vehicle per hour, how does the addition of one vehicle affect travel time?

b. If the traffic flow is 3400 vehicle per hour, how does the addition of one vehicle affect travel time?

c. Using your answer of parts a and b, discuss how travel time in central London are affected by increasing traffic flow.

EXAMPLE 5.18 DRIVING IN LONDON

The time $t$, in minutes, required to drive $1\text{ mile}$ in central London is given approximately by the formula

$t=\frac{600}{280-0.08q}$,

where $q$ is the traffic flow measured in vehicles per hour. The formula is valid as long as $280-0.08q$ is positive.