Two men starting from the same place walk at the rate of 5 kmph and 5.5 kmph respectively. What time will they take to be 8.5 km apart, if they walk in the same direction?

### Concept & Relative Speed When two bodies move in the same direction from the same starting point, their relative speed is the difference between their individual speeds. The distance separating them over time is governed by this relative speed. $$Time = \frac{Separation\ Distance}{Relative\ Speed}$$ ### Step-by-Step Solution 1. **Identify speeds:** Speed of first man = 5 kmph, Speed of second man = 5.5 kmph. 2. **Calculate relative speed:** Since they move in the same direction, Relative Speed = $5.5 \text{ kmph} - 5 \text{ kmph} = 0.5 \text{ kmph}$. This means they separate by 0.5 km every hour. 3. **Determine required separation:** The target distance apart is 8.5 km. 4. **Calculate time:** Time taken to achieve this separation = (Total Distance) / (Relative Speed). $$Time = \frac{8.5}{0.5} = \frac{85}{5} = 17 \text{ hours}$$ ### Exam Strategy & Shortcut Direct calculation without writing steps: $8.5 / (5.5 - 5) = 8.5 / 0.5 = 17$. Treat 0.5 as $1/2$, so $8.5 \times 2 = 17$. ### Common Pitfall A common mistake is adding the speeds instead of subtracting them, which is the rule for objects moving in opposite directions, not the same direction. ### Final Answer Therefore, the correct answer is **17 hrs**.