Answer:
A. 36 minutes
B. 120 minutes
C.
i. 144 minutes
ii. 984 minutes
D. Car 1 is 1.67km ahead of Cat 2 when Car 2 passed the toll B.
E. 98.33km
Explanation
A.
Given
dAb = 10km
dBc = 10km
Propagation Speed = 100km/hr
Delay time = 1 minute
Numbers of cars = 8
Number of tolls = 3
Total End to End delay = Propagation delay + Transition delay
Calculating Propagation Delay
Propagation delay = Total Distance/Propagation speed
Total distance = 10km + 10km = 20km
So, Propagation delay = 20km/100km/hr
Propagation delay = 0.2 hour
Translation delay = delay time* numbers of tolls * numbers of cars
Transitional delay = 1 * 3 * 8
Transitional delay = 24 minutes
Total End delay = 24 minutes + 0.2 hours
= 24 minutes + 0.2 * 60 minutes
= 24 minutes + 12 minutes
= 36 minutes
B.
Total End to End delay = Propagation delay + Transition delay
Calculating Propagation Delay
Propagation delay = Total Distance/Propagation speed
Total distance = 10km + 10km = 20km
So, Propagation delay = 20km/100km/hr
Propagation delay = 0.2 hour
Translation delay = delay time* numbers of tolls ------ Cars traveling separately
Transitional delay = 1 * 3
Transitional delay = 3 minutes
Total End delay for one car = 3 minutes + 0.2 hours
= 3 minutes + 0.2 * 60 minutes
= 3 minutes + 12 minutes
= 15 minutes
Total End delay for 8 cars = 8 * 15 = 120 minutes
C.
Given
dAb = 100km
dBc = 100km
Propagation Speed = 100km/hr
Delay time = 1 minute
Numbers of cars = 8
Number of tolls = 3
i. Cars travelling together
Total End to End delay = Propagation delay + Transition delay
Calculating Propagation Delay
Propagation delay = Total Distance/Propagation speed
Total distance = 100km + 100km = 200km
So, Propagation delay = 200km/100km/hr
Propagation delay = 2 hours
Translation delay = delay time* numbers of tolls * numbers of cars
Transitional delay = 1 * 3 * 8
Transitional delay = 24 minutes
Total End delay = 24 minutes + 2 hours
= 24 minutes + 2 * 60 minutes
= 24 minutes + 120 minutes
= 144 minutes
ii. Cars travelling separately
Total End to End delay = Propagation delay + Transition delay
Calculating Propagation Delay
Propagation delay = Total Distance/Propagation speed
Total distance = 100km + 100km = 200km
So, Propagation delay = 200km/100km/hr
Propagation delay = 2 hours
Translation delay = delay time* numbers of tolls ------ Cars traveling separately
Transitional delay = 1 * 3
Transitional delay = 3 minutes
Total End delay for one car = 3 minutes + 2 hours
= 3 minutes + 2 * 60 minutes
= 3 minutes + 120 minutes
= 123 minutes
Total End delay for 8 cars = 8 * 123 = 984 minutes
D.
Distance = 100km
Time = 1 min/car
Car 1 is 1 minute ahead of car 2 --- at toll A and B
If car 1 leaves toll B after 10 minutes then cat 2 leaves after 11 minutes
Time delay = 11 - 10 = 1 minute
Distance = time * speed
= 1 minute * 100km/hr
= 1 hr/60 * 100 km/hr
= 100/60
= 1.67km
E.
Given
Distance = 100km
Distance behind = 1.67
Maximum value of dBc = 100km - 1.67km = 98.33km
The maximum distance that can be reached is 98.33km
