Two towns `A` and `B` are connected by a regular bus service with a bus leaving in either direction every `T` min `A` man cycling with a speed of `20 km h^(-1)` in the direction `A` to `B` notices that a bus goes past him every `18 min` in the direction of his motion, and every `6 min` in the opposite direction. What is the period `T` of the bus service and with what speed (assumed constant )do the buses ply on the road?

Explanation

To solve the problem, we need to determine the period \( T \) of the bus service and the speed \( V \) of the buses. Let's break it down step by step.

### Step 1: Understand the Problem
We have a man cycling from town A to town B at a speed of \( 20 \, \text{km/h} \). He notices that buses pass him every \( 18 \) minutes from behind (A to B) and every \( 6 \) minutes from the front (B to A). We need to find the time period \( T \) of the bus service and the speed \( V \) of the buses.

### Step 2: Set Up the Relative Speeds
1. **Speed of the man**: \( v_m = 20 \, \text{km/h} \)
2. **Speed of the buses**: \( V \, \text{km/h} \)
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