Question

A particular one mile stretch of highway is known to get too congested when there are 200 or more cars on it at any one instant in time, resulting in a traffic jam. The normal speed limit is 60 miles/hour and you can assume that cars drive the normal speed limit as long as there is no congestion. It is currently 1PM and the arrival rate is 50 cars per minute. The arrival rate is going to increase constantly (but not necessarily linearly) until 6PM when it will be 300 cars per minute. At what arrival rate can a traffic jam be expected?

the answer is 200. I just need to know it it is solved.

Answer 1

A traffic jam on the one mile stretch of highway is expected when the arrival rate reaches 200 cars per minute, given that each car takes one minute to travel the mile at the speed limit of 60 miles per hour.

Step-by-step explanation:

The question asks at what arrival rate of cars a traffic jam can be expected on a one mile stretch of highway when the congestion threshold is 200 cars. Given that the arrival rate is 50 cars per minute and will rise to 300 cars per minute by 6PM, we need to determine the arrival rate at which 200 cars would simultaneously be on the one-mile stretch, assuming they are traveling at the normal speed limit of 60 miles per hour. Since a car covers one mile in one minute at the speed of 60 miles per hour, it means the road will reach maximum capacity and get congested when the arrival rate is 200 cars per minute, not the 50 cars per minute as it is at 1PM.