Consider the car-caravan analogy from Section 4 in Chapter 1. In this problem, a
ID: 3890146 • Letter: C
Question
Consider the car-caravan analogy from Section 4 in Chapter 1. In this problem, assume a propagation speed of 75 km/hr and that each toll booth takes 15 seconds to service a car.
a) Suppose the caravan of 10 cars travels a total of 100 km beginning immediately in front of the first toll booth, travels 50 km to a second toll booth, then another 50 km to a third toll booth, and finally stops immediately after the third tool booth. What is the total end-to-end delay?
b) Where is the last car in the caravan after 45 minutes? Your answer must include a distance/specific location, and not only a relative direction.
Explanation / Answer
a)
Distance between each consecutive toll is 50 km.
total end to end delay = propagation delay + transmission delay
propagation delay between two tolls = 50 / 75 = 0.67 hr
There are two tolls , So total propagation delay = 0.67*2 = 1.34 hr = 80 minutes
Transmission delay of 1 car = 15 seconds = 15/60 = 0.25 minutes.
Total 10 cars are there so Total transmission delay = 0.25*10 = 2.5 min at each toll
So end to end delay = 80 + 2.5 + 2.5 + 2.5 = 87.5 minutes.
b)
Propagation delay between 3 tolls is 80 minutes .
No suppose the carvan started at first toll and time taken to reach second toll
= 2.5 min( transmission delay of first toll) + 40 minutes ( propagation delay from first toll to second toll i.e. 50/75 * 60) + 2.5 min ( transmisison delay of second toll) = 45 minutes
So after 45 minutes,last car has just crossed the second toll So they have travelled 50 kms.