Rehman walks at 8 km/h and Roma cycles at 13 km/h towards each other. If they meet after 36 minutes, what distance in kilometres initially separated them?

Introduction / Context:
This is a classic relative speed problem from time, speed, and distance. Two people move towards each other from opposite directions, and you are given their speeds and the time until they meet. The concept of relative speed allows you to treat the situation as if one person is stationary and the other is moving at the sum of their speeds, which simplifies the calculation of the initial distance between them.

Given Data / Assumptions:

• Rehman walks at 8 km/h.
• Roma cycles at 13 km/h.
• They are moving directly towards each other.
• They meet after 36 minutes.
• We must find the initial distance between them in kilometres.

Concept / Approach:
When two objects move towards each other along a straight line, their relative speed is the sum of their individual speeds. Distance covered before they meet is then relative speed multiplied by time. Since the time is given in minutes, it must be converted to hours to match the units of km/h. Once we find the distance using Distance = Speed * Time, we simply express it to one decimal place as needed.

Step-by-Step Solution:
Compute the relative speed: 8 km/h + 13 km/h = 21 km/h.Convert time from minutes to hours: 36 minutes = 36/60 hours = 0.6 hours.Use the formula Distance = Speed * Time with relative speed.Distance = 21 km/h * 0.6 h = 12.6 km.Therefore, the initial distance between Rehman and Roma was 12.6 kilometres.

Verification / Alternative check:
We can split the total distance into individual portions covered by each person. In 0.6 hours, Rehman walking at 8 km/h covers 8 * 0.6 = 4.8 km. Roma cycling at 13 km/h covers 13 * 0.6 = 7.8 km. Adding these gives 4.8 + 7.8 = 12.6 km, which matches the distance computed via relative speed. This double check confirms the calculation is correct.

Why Other Options Are Wrong:

• 18.9 km and 15.8 km are larger than the correct distance and would require either more time or higher speeds.
• 9.5 km and 21.0 km do not match the product of relative speed and time and fail the individual distance split check.
• Only 12.6 km satisfies both the relative speed formula and the individual distance calculations.

Common Pitfalls:

• Forgetting to convert minutes into hours, which changes the distance by a factor of 60.
• Incorrectly subtracting the speeds instead of adding them when the persons move towards each other.
• Making arithmetic mistakes in multiplying 21 by 0.6 or adding the individual distances.

Final Answer:
12.6 km