Walking rate vs time for same distance: The walking rates of A and B are in the ratio 2 : 3. If B takes 36 minutes to cover a fixed distance, how long does A take for the same distance?

Introduction / Context:
For equal distances, time is inversely proportional to speed (or rate). If two people have a known rate ratio, their required times will be in the inverse ratio.

Given Data / Assumptions:

• Rate(A) : Rate(B) = 2 : 3.
• Time is inversely proportional to rate.
• Time(B) = 36 minutes.

Concept / Approach:
Time(A) : Time(B) = 3 : 2. With Time(B) = 36 representing 2 parts, compute the value of one part and then scale up for A’s time (3 parts).

Step-by-Step Solution:
Let the time ratio be 3 : 2 (A : B).2 parts = 36 ⇒ 1 part = 18.A’s time = 3 parts = 54 minutes.

Verification / Alternative check:
Pick a distance, say 6 km. If A’s rate = 2 units and B’s rate = 3 units, then T(A) = 6/2 = 3 units of time and T(B) = 6/3 = 2 units. Scaling to B = 36 gives A = 54.

Why Other Options Are Wrong:

• 24 and 21.6 are smaller than B’s time despite A being slower.
• 48 assumes a 4 : 3 inverse instead of 3 : 2.

Common Pitfalls:

• Using direct instead of inverse proportion.

Final Answer:
54min