Speed–time inverse relation Two trains A and B travel from X to Y with speed ratio A:B = 2:7. What is the ratio of their times to cover the same distance?

Introduction / Context:
For fixed distance, time is inversely proportional to speed. If one vehicle is faster by a factor, it takes proportionally less time.

Given Data / Assumptions:

• Speed ratio A:B = 2:7.
• Distance X→Y is the same for both.

Concept / Approach:
If vA:vB = 2:7, then tA:tB = 1/2 : 1/7 = 7 : 2 after scaling to integers.

Step-by-Step Solution:

Verification / Alternative check:
Assume any convenient common distance, e.g., 14 units. A takes 14/2 = 7 units of time; B takes 14/7 = 2 units ⇒ 7:2.

Why Other Options Are Wrong:
Other ratios don’t match the strict inverse of 2:7.

Common Pitfalls:
Keeping the same 2:7 ratio for time; that’s only valid when distances differ, not here.

Final Answer:
7 : 2