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 \( V_0 \) of the buses.

### Step 1: Define the known variables
- Speed of the man cycling, \( v_m = 20 \, \text{km/h} \)
- Time interval for buses passing in the same direction, \( t_1 = 18 \, \text{min} \)
- Time interval for buses passing in the opposite direction, \( t_2 = 6 \, \text{min} \)

### Step 2: Convert time intervals from minutes to hours
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