The top of a ladder 6 metres long is resting against a vertical wall on a level pavement, when the ladder begins to slide outwards. At the moment when the foot of the ladder is 4 metres from the wall, it is sliding away from the wall at the rate of 0.5 m/sec. How fast is the top-sliding downwards at this instance? How far is the foot from the wall when it and the top are moving at the same rate?

Explanation

To solve the problem step by step, we can follow this structured approach:

### Step 1: Understand the scenario
We have a ladder of length 6 meters leaning against a wall. The foot of the ladder is sliding away from the wall, and we need to find how fast the top of the ladder is sliding downwards when the foot is 4 meters away from the wall.

### Step 2: Set up the relationship
Let:
- \( X \) be the distance from the wall to the foot of the ladder.
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