The travel-rate ratio of A to B is 2 : 3, so A takes 20 minutes more than B to reach the same destination. If A had walked at double speed, how long would A take to cover the distance?

Introduction / Context:
Time to cover a fixed distance is inversely proportional to speed. With a speed ratio 2:3 (A slower than B), and a 20-minute time difference, we can back out a scale for distance/speed and then compute A’s time at doubled speed. This avoids finding the absolute distance explicitly.

Given Data / Assumptions:

• A:B speed ratio = 2:3 ⇒ let speeds be 2k and 3k.
• Time difference = 20 min = 1/3 h.
• Distance for both is the same.

Concept / Approach:
Times: t_A = D/(2k), t_B = D/(3k). Difference t_A − t_B = D/(6k) = 1/3 ⇒ D/k = 2. Doubling A’s speed to 4k makes new time t_A’ = D/(4k) = (D/k)/4.

Step-by-Step Solution:

Verification / Alternative check:
Original times: D/(2k) = 1 h and D/(3k) = 2/3 h (difference 1/3 h = 20 min), consistent with D/k = 2.

Why Other Options Are Wrong:
35, 20, 45 min do not equal the implied 1/2 hour at doubled speed.

Common Pitfalls:
Applying the 2:3 ratio to time instead of speed (they are inversely related).

Final Answer:
30 min