Party A and Party B set out from AB, and the speed of Party A was 4/5 of that of Party B. After arriving at the places of Party B and Party A, Party A returned to AB, and the speed of Party A increased by 1/4, and that of Party B increased by 1/3. It is known that the two meeting points of A and B are 34 kilometers apart. How to find the distance between AB?

Solution: Take the whole journey as the unit 1.

Because time is constant, the distance ratio is the speed ratio.

Distance ratio of Party A and Party B = speed ratio = 4: 5

B's speed is fast, B reaches point A, and A travels 1×4/5=4/5.

At this time, Party B speeds up 1/3, so the speed ratio of Party A and Party B is 4: 5× (1+ 1/3) = 3: 5.

A left 1-4/5= 1/5, so b left (1/5)/(3/5)= 1/3.

At this time, A accelerates and the speed ratio changes from 3: 5 to 3 (1+ 1/4): 5 = 3: 4.

The distance between Party A and Party B is 1- 1/3=2/3.

When meeting, Otsuichi left1/3+(2/3) × 4/(3+4) =1/3+8/21= 5/7.

That is, 5/7 of the distance a.

The meeting point for the first time is 4/9 of the distance a.

Then AB distance = 34/(5/7-4/9) = 34/(17/63) =126km.

for reference only