1, two cars, A and B, respectively, travel in opposite directions from AB at the same time. Car B travels more than car A per hour 1/20, and the two cars travel 9/20 of the whole journey per hour. They walked on after meeting for the first time on the road. A arrives at B, B returns immediately after arriving at A, and meets again on the way, if two cars meet 40 kilometers apart. How many kilometers are the two places apart?

At the same time, two trains, A and B, are running in two opposite directions, B and C respectively. It is known that the distance between AB is 9/ 10 of the AC distance. When car A travels 60 kilometers, the ratio of the distance traveled by car B to the remaining distance is 1: 3. At this time, the distance between the two trains and the destination is equal. Find the communication distance. (column description)

Set the x of the whole train of B every hour.

The topic is x+(x+ 1/20)=9/20 x=4/20.

X+ 1/20=5/20

That is, 4/20 of the whole journey of A and 5/20 of the whole journey of B.

Because two cars travel 9/20 of the whole distance every hour, it takes 1/(9/20)=20/9 hours for two cars to complete the distance.

So when we first met:

A left (4/20)*(20/9)=4/9.

B Left (5/20)*(20/9)=5/9.

That is, they met for the first time at a distance of 4/9.

When they met for the second time, they walked three times together.

now

A * * * Left (4/9)*3=4/3.

At this time, the distance between A and B is 4/3- 1= 1/3 of the whole journey.

Otsuichi * * * Left (5/9)*3=5/3

At this time, the distance from A to A is 5/3- 1=2/3 of the whole journey.

That is, they met for the second time at a distance of 2/3.

The distance between two encounters is 2/3-4/9=2/9 of the whole journey.

So the distance between AB is 40/(2/9) = 180km.

2. Two trains, A and B, travel in the opposite direction from A at the same time, heading for B and C respectively. It is known that the distance between AB is 9/ 10 of the AC distance. When the A train travels 60 kilometers, the ratio of the distance traveled by the B train to the remaining distance is 1: 3, and the distances between the two trains to the destination are equal. Find the communication distance. (column description)

Let the AC distance be x, then we can know that the AB distance is 9/ 10x.

The ratio of the distance traveled by car B to the remaining distance is 1:3, which means that car B has traveled1/(1+3) =1/4, and the remaining 3/4.

At this time, the distance between the two trains and the destination is equal.

So there is 9/ 10x-60=3/4x, and the solution is: x=400.