Two men `Pa n dQ` start with velocity `u` at the same time from the junction of two roads inclined at `45^0` to each other. If they travel by different roads, find the rate at which they are being separated.

Explanation

To solve the problem step by step, we will follow the reasoning provided in the video transcript and derive the solution systematically.

### Step 1: Understand the Setup
Two men, P and Q, start from the same point (junction O) and travel along two roads that are inclined at an angle of 45 degrees to each other. They both have the same initial velocity \( u \).

### Step 2: Define the Distances
Let the distance traveled by both men after time \( t \) be represented as \( x \). Since they both travel with the same speed, we have:
\[
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