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 of finding the rate at which two men P and Q are being separated as they travel along two roads inclined at 45 degrees to each other, we can follow these steps:

### Step 1: Understand the Geometry
Two men P and Q start from a common point O and travel along two roads that form a 45-degree angle with each other. After time \( t \), both men will have traveled the same distance \( x \) in their respective directions.

### Step 2: Express the Distances
Since both men travel with the same velocity \( u \), the distance traveled by each man after time \( t \) can be expressed as:
\[
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