The speeds of three cars are in the ratio 2 : 3 : 5. For the same distance, what is the ratio of their times taken?

Introduction / Context:
For equal distances, time is inversely proportional to speed. Given a speed ratio, the time ratio is the inverse of those numbers.

Given Data / Assumptions:

• Speed ratio = 2 : 3 : 5.
• All travel the same distance.

Concept / Approach:
Time ∝ 1/speed, so time ratio = 1/2 : 1/3 : 1/5. Multiply by the LCM (30) to get whole numbers.

Step-by-Step Solution:

Verification / Alternative check:
Check intuition: the fastest car (5 parts) should have the smallest time (6 parts), which it does.

Why Other Options Are Wrong:
They place larger time for faster cars or mismatch the inverse relationship entirely.

Common Pitfalls:
Forgetting to invert ratios; accidentally copying the same 2:3:5 order for times.

Final Answer:
15 : 10 : 6