A `10-km` long straight road connects two towns `A` and `B`, Two cyclists dimultaneously start one from town `A` and the other from town `B` .On reaching the opposite town, a cyclists simmediaeately retrns to his starting town wheras the other cyclist takes some rest and then returns to his starting town. Both of them can ride at speed `20 km h^(-1)` in absence of wind but during their whole journey uniform wind from town `A` and `B` increase the speed of it decreases the speed of the cyclist going against the wind Both the cyclisrs meet twice, first at `2` km and then `6` km away from one of the tomns. If which town and for what perild does a cyclist rest ?

Explanation

To solve the problem step by step, we will analyze the motion of the two cyclists, their speeds, and the distances they travel.

### Step 1: Understand the Setup
We have two towns, A and B, connected by a 10 km road. Cyclist 1 starts from town A and Cyclist 2 starts from town B. Both cyclists ride at a speed of 20 km/h in still air. However, wind affects their speeds differently depending on their direction of travel.

### Step 2: Define Variables
Let:
- \( v = 20 \) km/h (speed of cyclists in still air)
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