Ali and Faizer are 27 m apart. When they walk in the same direction, they meet after 9 hours. When they walk in opposite directions, they meet after 3 hours. What is the walking speed of Ali (in m/h)?

Introduction / Context:
This problem tests understanding of relative speed in both same-direction and opposite-direction motion, with a twist that the speeds are in metres per hour and the initial separation is small compared to the time. The key idea is to form equations for the relative motion in both scenarios and solve for the individual speeds.

Given Data / Assumptions:

• Initial distance between Ali and Faizer = 27 m.
• They meet after 9 hours when walking in the same direction.
• They meet after 3 hours when walking in opposite directions.
• Speeds of Ali and Faizer are constant and in m/h.

Concept / Approach:
Let Ali's speed be a m/h and Faizer's speed be f m/h. When they move in the same direction, the relative speed is |a - f| and they close the 27 m gap in 9 hours, so |a - f| = 27 / 9 = 3 m/h. When they move in opposite directions, the relative speed is a + f and they meet in 3 hours, so a + f = 27 / 3 = 9 m/h. Solving these two equations gives Ali's speed.

Step-by-Step Solution:
From opposite directions: a + f = 9. From same direction: |a - f| = 3. Assume Ali is faster, so a - f = 3. Add the two equations: (a + f) + (a - f) = 9 + 3. This gives 2a = 12, so a = 6 m/h. Substitute back: 6 + f = 9, so f = 3 m/h.

Verification / Alternative check:
Same direction: relative speed = a - f = 6 - 3 = 3 m/h. Time to meet = distance / relative speed = 27 / 3 = 9 hours, matches given. Opposite directions: relative speed = a + f = 6 + 3 = 9 m/h. Time to meet = 27 / 9 = 3 hours, also matches. So the values are consistent.

Why Other Options Are Wrong:

• 9 m/h or 12 m/h as Ali's speed would not satisfy both meeting times when solving the equations.
• 3 m/h is actually Faizer's speed, not Ali's, under the assumption that Ali walks faster.

Common Pitfalls:
Some candidates mistakenly add speeds in the same direction instead of taking the difference. Others confuse which person is faster, but the question asks for Ali's speed, and the equations clearly show that a must be the larger one for consistent solutions. Keeping track of relative speeds in different directions is crucial.

Final Answer:
The walking speed of Ali is 6 m/h.