How to solve the problem of tunnel Olympic Games

Three problems of train tunnel (crossing bridge)

Basic problems: this kind of problems need to pay attention to two points: the length of the train is recorded in the total distance; The focus is on the rear of the train: the people who pass by the train, that is, the people on the left of the rear.

It took 50 seconds for the train to pass through a bridge with a length of1140m and 80 seconds to pass through a tunnel with a length of1980m. Find the speed and length of the train. (Bridge crossing problem)

It takes 55 seconds for a train to cross an 800-meter bridge and 40 seconds to cross a 500-meter tunnel. How many seconds does it take for this train to cross head-on with another train with a length of 384 and a speed of18m per second? (Trains meet)

(2) Wrong car or overtaking: See which car passes by, and the sum or difference of distance is the length of which car.

For example, the express train and the local train travel in the opposite direction. The length of the express train is 50 meters, the length of the local train is 80 meters, and the speed of the express train is twice that of the local train. If it takes five seconds for a person sitting in the local train to see the express train pass through the window, how long does it take for a person sitting in the local train to see the local train pass through the window?

(3) Comprehensive question: Seek the speed together with the conductor; Although we don't know the total distance, we can find the distance relationship between two people or cars at a certain moment.

Illustration

A tunnel is 360 meters long. It takes 8 seconds for a train to enter the tunnel from the front and 20 seconds from the front to the whole train. How long is this train?

On a path parallel to the railway, a group of people and cyclists were driving south at the same time. The pedestrian speed is 3.6 km/h and the cyclist speed is 10.8km/h when a train comes from behind them. It takes 22 seconds for a train to overtake a pedestrian and 26 seconds for a cyclist. What is the total length of the train?

Solving this problem is a catch-up problem. The pedestrian speed is 3.6 km/h = 1 m/s, the cyclist speed is 10.8 km/h =3 m/s, and the length of the train body is equal to the distance difference between the train tail and pedestrians, as well as the distance difference between the train tail and cyclists. If the speed of the train is assumed to be x m/s, then the body length of the train can be expressed as (x- 1)×22 or (x-3)×26, so it is not difficult to list the equations.

Method 1: Let the speed of this train be x m/s, and make an equation according to the meaning of the question.

(x- 1)×22=(x-3)×26 .

The solution is x= 14. So the length of the car body is (14- 1)×22=286 (m).

Method 2: directly set the length of the train as x, then the equivalence relationship lies in the speed of the train.

Available: x/26+3 = x/22+ 1.

This can also be done directly, x=286 meters.

Method 3: Since the distance is the same, we can also use the inverse ratio of speed and time to solve it.

The catch-up time ratio is 22: 26 =11:13.

So we can get: (v car-1): (V car -3) = 13: 1 1.

Available v cars = 14m/s

So the length of the train is (14- 1)×22=286 (meters).

A: This train is 286 meters long.

It takes 25 seconds for a train to pass through a 250-meter-long tunnel and 23 seconds for a 2 10-meter iron bridge. How many seconds does it take for this train to cross another train with a length of 320 meters and a speed of 64.8 kilometers per hour?

Answer the question of the train crossing the bridge

Formula: (train length+bridge length)/train speed = train passing time.

A train with a speed of 64.8 kilometers per hour has a speed of 18 meters per second.

It takes 25 seconds for a train to pass through a 250-meter-long tunnel and 23 seconds to pass through a 2 10-meter railway bridge.

Train speed: (250-210)/(25-23) = 20m/s.

Distance difference divided by time difference equals train speed.

Train length: 20*25-250=250 (m) or 20*23-2 10=250 (m).

Therefore, it takes (320+250)/(18+20) =15 (seconds) for this train to cross another train with a length of 320m and a speed of 64.8km/h.

Example 4 A train is160m long and runs at a constant speed. First, it takes 26s to pass through the tunnel A (that is, from the front entrance to the back exit). After driving 100km, it takes 16s to reach station A through tunnel B, with a total journey of100.352km. What is the length of tunnels A and B?

The length of tunnel a should be xm.

Then the length of tunnel B is (100.352- 100) (in kilometers! )* 1000-x=(352-x)

Then (x+160)/26 = (352-x+160)/16 gives x = 256.

Then the length of tunnel B is 352-256=96.

The basic formula of the train crossing the bridge problem is: (the length of the train+the length of the bridge)/time = speed Example 4: A and B walk along the railway track in opposite directions. At this moment, a train is coming towards A at a constant speed. The train passes A 15 seconds, and then B 17 seconds. It is known that both of them walk at a speed of 3.6 kilometers.

Answer from the meaning of the question, A and the train are a meeting problem, and the sum of their traveling distances is the length of the train. B and the train are a catching-up problem, and the difference between their travel distances is the length of the train. Therefore, we assume that the speed of this train is χ m/s, and the walking speed of both trains is 3.6 km/h = 1 m/s, so the length of the train is calculated as (15 χ+1x15) meters according to the encounter between A and the train.

15χ+/kloc-0 /×15 =17χ-17 solution: χ = 16.

Therefore, the train length is17×16-/kloc-0 /×17 = 255 meters.