A cyclist travels at a speed of $X$ km/h for 2 hours. The cyclist then increases their speed by 2 km/h and travels for another 3 hours. The total distance covered is 36 km. We need to find the initial speed, $X$.

1. Problem Description

A cyclist travels at a speed of $X$ km/h for 2 hours. The cyclist then increases their speed by 2 km/h and travels for another 3 hours. The total distance covered is 36 km. We need to find the initial speed, $X$.

2. Solution Steps

The formula for distance is:

$Distance = Speed \times Time$

The distance covered in the first 2 hours is $2 \times X = 2X$ km.

The speed in the next 3 hours is $X + 2$ km/h.

The distance covered in the next 3 hours is $3 \times (X + 2) = 3X + 6$ km.

The total distance is $2X + 3X + 6$ km, which is given as 36 km.

Therefore,

$2X + 3X + 6 = 36$

$5X + 6 = 36$

$5X = 36 - 6$

$5X = 30$

$X = \frac{30}{5}$

$X = 6$

3. Final Answer

The initial speed $X$ is 6 km/h.

The answer is D.