How would you describe the capacity of a road? For simplicity, think of a one la
ID: 3110889 • Letter: H
Question
How would you describe the capacity of a road? For simplicity, think of a one lane road in one direction. You may come to the conclusion that it depends on the speed of vehicles. Say that all vehicles move at 60 mph. Now you might want the distance between vehicles. Think of vehicles as points, with say 30 feet between them. Now how many vehicles pass through this lane in one hour? What if the distance between them is doubled? Instead, what if speed is halved? (In each case, what is the new throughput – i.e. number of vehicles that pass through the lane in one hour)? Finally, do you think there is a relationship between the distance between vehicles and the speed of traffic? How would you characterize that?
Explanation / Answer
Speed of each vehicle is 60 mph.
Distance between two vehicles = 30 feet = 30/5280 miles
Total distance travelled in one hour = speed*time = 60*1 = 60 miles.
We know that the distance between two vehicles = 1/176 miles.
Therefore, the total number of cars passing the lane in 1 hour = 60/(1/176) = 60*176 = 10560 cars
Therefore, 10560 cars pass the lane in 1 hour.
If distance between the cars is doubled, the number of cars passing the lane would get halved. We will have 5280 cars passing the lane in an hour if distance between the cars is doubled.
If speed of the cars is halved, then the distance travelled by them in one hour will get halved. Which will reduce the total number of cars passing the lane by half. Hence, 5280 cars will pass the lane in an hour if speed of vehicles is halved.
Yes, the throughput remains equal in both the cases.
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