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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.