Question

Assume a propagation speed of 200 km/hour.
a. Suppose the caravan travels 180 km, beginning in front of one tollbooth, passing through a second tollbooth, and finishing just after a third tollbooth. What is the end-to-end delay?
b. Repeat (a), now assuming that there are twelve cars in the caravan instead of ten.

Answer 1

Given that

Propagation speed 200 km /h

distance traveled by car d = 180 km

propagation delay t = 180 / 200 = 0.9 hours = 54 minutes

Time taken by tollbooth to service  a car = 12 sec

we have ten cars so  total time taken by each tollbooth to service 10 cars = 12*10 = 120 seconds

Now time taken by all three tollbooth to service all ten cars =120*3 = 360 seconds = 6 minutes

So end to end delay = Propagation delay + time taken by all three tollbooth to service all ten cars

= 54+6 = 60 minutes = 1 hour

b)

We have 12 cars instead of 10

d = 180km

Propagation delay t = 54 minutes

Time taken by a tollbooth to service 12 cars = 12*12 = 144 seconds

Time taken by all three tollbooth to service 12 cars = 144*3 = 432 seconds = 7 minutes 12 seconds

End to end delay = t + Time taken by all three tollbooth to service 12 cars

End to end delay = 54 minutes +7 min 12 seconds = 1 hour 1 minute 12 second

Good Luck !!