Consider a typical station, where passengers have to get off and then take the stairs to the exit on the upper floor. Usually these trains are very crowded, so when the train arrives at the station, a large number of passengers will go up the stairs at the same time, forming a "crowd", and the stairs can accommodate two rows of people. On both sides of most platforms are two adjacent train tracks running in opposite directions. In the worst case, if two trains arrive at the same time, it will take a long time for all passengers to leave the station.
Suppose that the commuter train has n cars, each car is d in length, the platform is p in length, and the number of stairs at the exit stairs is q.
Please establish a mathematical model to estimate the time required for a passenger to arrive at the exit from the train, find out the data by yourself, and use your model to calculate the passenger's departure time under the following circumstances:
1. A fully loaded train arrived at the station. Passengers got off the train and climbed the stairs to leave the station.
2. Two full trains arrive at the station, and passengers * * * use one platform. Passengers got off the train and climbed the stairs to get out of the station.
3. If the location of the stairs on the platform can be redesigned, where should the stairs be located to minimize the departure time of passengers on one or two trains?
4. How does the number of stairs reaching the street affect the departure time?
5. If the stairs can accommodate K people, and K is an integer greater than 1, what will happen to the departure time? This is a mathematical modeling problem. What does it mean? How should I write it?
Many commuter subway trains run from the suburbs of big cities to the city center, and most of them are more than 10 knots. Each train has only two exits, close to both ends of the train, so that the train can carry as many passengers as possible, and passengers need to walk a long distance to leave the train. Each carriage has a middle aisle, with three seats on one side and two seats on the other.
Consider a typical station, where passengers have to get off and then take the stairs to the exit on the upper floor. Usually these trains are very crowded, so when the train arrives at the station, a large number of passengers will go up the stairs at the same time, forming a "crowd", and the stairs can accommodate two rows of people. On both sides of most platforms are two adjacent train tracks running in opposite directions. In the worst case, if two trains arrive at the same time, it will take a long time for all passengers to leave the station.
Suppose that the commuter train has n cars, each car is d in length, the platform is p in length, and the number of stairs at the exit stairs is q.
Please establish a mathematical model to estimate the time required for a passenger to arrive at the exit from the train, find out the data by yourself, and use your model to calculate the passenger's departure time under the following circumstances:
1. A fully loaded train arrived at the station. Passengers got off the train and climbed the stairs to leave the station.
2. Two full trains arrive at the station, and passengers * * * use one platform. Passengers got off the train and climbed the stairs to get out of the station.
3. If the location of the stairs on the platform can be redesigned, where should the stairs be located to minimize the departure time of passengers on one or two trains?
4. How does the number of stairs reaching the street affect the departure time?
5. If the stairs can accommodate K people, and K is an integer greater than 1, what will happen to the departure time?