1.) In this problem, assume a propagation speed of 100 km/hr and that each toll
ID: 3785887 • Letter: 1
Question
1.) In this problem, assume a propagation speed of 100 km/hr and that each toll booth takes 30 seconds to service a car.
a) (7 points) Suppose the caravan travels 160 km beginning immediately in front of the first toll booth, travels 80 km to a second toll booth, then another 80 km to a third toll booth, and finally
stops immediately after the third tool booth. What is the total end-to-end delay?
b) (4 points) Where is the last car in the caravan after 60 minutes? Your answer must include a distance/specific location, and not only a relative direction.
Explanation / Answer
a)
propogation spedd =100km/hrs
caravan travels=160 km to 1st tollbooth+80 km to 2nd tollbooth+80 km to 3rd tollbooth
distance between two tollbooth = 80km
Dprop=80km/100kph = 0.80 hrs = 48 mins between each tollbooth or 160 mins from 1st to last tollbooth
Dtrans at 1st tollbooth = 30 secs = 30/60= 0.5mins
therefore (0.5 *10)=5 mins for the caravan to clear tollbooth (suppose there are 10 cars in the tollbooth)
end to end delay= Dprop+Dtrans= 160mins+(5*3) mins where 3 is the number of tollbooth
=160+15=175mins
b) assuming there are total 10 cars
at the 1st toll booth the 10th cars will have delay of 5mins (Dtrans at tollbooth 1st=0.5mins, or 0.5*10=5mins for 10 cars assuming the 10th car is the last one), therefore 5 mins will be the Ddtrans for the 10th cars.
Dprop for the last cars from 1st toll booth to 2ns toll booth = 48mins
at 2nd toll booth the 10th car will take 5 mins
therefore the total Dtrans= 5+5=10mins
and Dprop=48mins
last car will clear the 2nd toll booth in 48+10=58mins
after 60 mins the last car have just cleared the 2nd toll booth 2mins ago.
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