Two boys start walking from the same place in the same direction at constant speeds of 5 km/h and 5.5 km/h respectively. After how many hours will the distance between them become 8.5 km, assuming that both boys continue walking at their given speeds in the same direction?

Introduction / Context:
This time and distance question focuses on relative speed when two people move in the same direction. We are asked to determine how long it takes for the gap between them to become 8.5 km, given that one person walks slightly faster than the other.

Given Data / Assumptions:

• Both boys start from the same place at the same time.
• Slower boy speed = 5 km/h.
• Faster boy speed = 5.5 km/h.
• They move in the same direction along a straight path.
• We want the time until they are 8.5 km apart.

Concept / Approach:
When two objects move in the same direction, the rate at which the distance between them increases is given by their relative speed, which is the difference between their speeds. Here, only the faster boy is pulling away, so we use relative speed = 5.5 - 5 km/h. Then, time to reach a certain separation is distance divided by relative speed.

Step-by-Step Solution:
Relative speed when walking in the same direction = 5.5 km/h - 5 km/h = 0.5 km/h. Required separation between the boys = 8.5 km. Time taken to achieve this separation = distance / relative speed. So, t = 8.5 / 0.5 hours. Compute t = 8.5 * 2 = 17 hours. Therefore, it will take 17 hours for the boys to be 8.5 km apart.

Verification / Alternative check:
After 17 hours, the slower boy travels 5 * 17 = 85 km. The faster boy travels 5.5 * 17 = 93.5 km. The difference between 93.5 km and 85 km is 8.5 km, confirming the required separation.

Why Other Options Are Wrong:
At 15, 16 or 18 hours, the distance difference does not equal 8.5 km: it would be 7.5 km, 8 km or 9 km respectively. The 20 hour option gives a separation of 10 km. Only 17 hours produces the exact 8.5 km difference indicated in the question.

Common Pitfalls:
Learners sometimes add the speeds instead of subtracting when both objects move in the same direction. Another common mistake is to mis-handle the decimal relative speed. Always remember that for same direction motion, relative speed is the difference between speeds, not the sum.

Final Answer:
The distance between the boys becomes 8.5 km after 17 hours.