A car is traveling on a straight road on a stretch that contains towns a, b, c,
ID: 1410125 • Letter: A
Question
A car is traveling on a straight road on a stretch that contains towns a, b, c, and D as illustrated below. The car is between towns A and D. A B C D Town A is 60 miles from Town D. with Town B 20 miles from towns A and C and Town C 20 miles from Town D. It is an otherwise rural area and there arc cell phone towers only in each of the four towns. Each lower has a range of ten miles. 1. Suppose that the car is traveling at a uniform rate of 55 miles per hour. What percentage of the time for the trip between towns A and D is spent within range of the tower in Town A? Town B? 2. Suppose that the velocity of the car is r(t) ={60t. t lessthanorequalto 1 120-60t, t Greaterthanorequalto 1 where t is measured in hours and r(t) is measured in miles per hour. Also, suppose that at t =0. the car is at Tow n A. Now. what percentage of the time for the trip between towns A and D is spent with in range of the tower in Town A? Town B? 1.Given the velocity of the car as described in part 2. do you think that you could move the towers to other locations in such a way that the car would spend the same amount of time with in range of each lower? If so. justfy your answer. If not. explain why not. 2.Below is a graph of a velocity of a car as it travels between Town A and Town D. What percentage of the lime is spent wilhin range of Town B?Explanation / Answer
1) Percentage time range of tower in town A = (0.1818/1.0909) * 100
= 16.66 %
Percentage time range of tower in town B = (0.3636/1.0909) * 100
= 33.33 %
2) Percentage time range of tower in town A = ( 0.6 * 0.1818/1.0909) * 100
= 9.996 %
Percentage time range of tower in town B = (1.2 * 0.3636/1.0909) * 100
= 39.996 %
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