Two men A and B start from the same place X and walk in the same direction. A walks at 4.5 km/h and B walks at 5.75 km/h. How far apart will they be after 3.5 hours of walking?

Introduction / Context:
This question explores the concept of relative speed when two people move in the same direction. It checks if students can compute individual distances traveled, use the difference in speed to find how far apart the walkers are, and handle fractional speeds and times correctly. This type of problem is very common in time and distance sections of aptitude exams.

Given Data / Assumptions:

• Speed of A = 4.5 km/h.
• Speed of B = 5.75 km/h.
• Both start from the same point X at the same time.
• They walk in the same direction for 3.5 hours.
• We assume constant speeds throughout.
• We need the distance between A and B after 3.5 hours.

Concept / Approach:
When two people move in the same direction, the distance between them after a certain time is based on their relative speed. The relative speed in this case is the difference between their individual speeds. The separation between them after a given time is equal to relative speed multiplied by time. It is often easier to work with decimal or fractional representations of mixed numbers.

Step-by-Step Solution:
Speed of A = 4.5 km/h. Speed of B = 5.75 km/h. Relative speed (B compared to A) = 5.75 - 4.5 = 1.25 km/h. Time of walking = 3.5 hours. Distance between them after 3.5 hours = relative speed * time. Distance between them = 1.25 * 3.5 km. 1.25 * 3.5 = (5 / 4) * (7 / 2) = 35 / 8 = 4.375 km. 4.375 km is equal to 4 3/8 km.

Verification / Alternative check:
We can also compute individual distances. In 3.5 hours, A covers 4.5 * 3.5 = 15.75 km, and B covers 5.75 * 3.5 = 20.125 km. The difference between 20.125 km and 15.75 km is 4.375 km, again equal to 4 3/8 km. This confirms that our relative speed method is correct and that the two approaches give the same result.

Why Other Options Are Wrong:
2 9/7 km, 3 7/5 km, 1 3/4 km, and 3 1/2 km are all distances that do not match the product of 1.25 km/h and 3.5 hours. Substituting these values backward into speed = distance / time does not give the correct relative speed of 1.25 km/h, so these options are inconsistent with the given data.

Common Pitfalls:
Students sometimes add the two speeds instead of subtracting them when the movement is in the same direction. Another common error is misreading 4.5 and 5.75 as whole numbers or mismanaging the fractional multiplication. Converting mixed numbers to improper fractions or decimals before performing operations helps to avoid calculation mistakes.

Final Answer:
After 3.5 hours, A and B are 4 3/8 km apart.