Comparing speeds when half distance takes double time A distance is covered at speed v1. If half that distance is covered in double the original time, what is the ratio v1 : v2 of the two speeds?

Introduction / Context:
This revisits proportional reasoning with distance and time. When the new scenario covers half the distance in twice the time, the speed reduces by a factor of 4 relative to the original.

Given Data / Assumptions:

• Original speed v1 = D / T.
• New speed v2 = (D/2) / (2T).

Concept / Approach:
Simplify v2 to express it as a multiple of v1 and form the ratio.

Step-by-Step Solution:

Verification / Alternative check:
Plug D = 4, T = 1 ⇒ v1 = 4. New case: 2 units in 2 h ⇒ v2 = 1. Ratio 4:1.

Why Other Options Are Wrong:
1:2 or 2:1 confuse which quantity changed and by what factor.

Common Pitfalls:
Thinking “half distance, double time ⇒ half/double = quarter” but then inverting incorrectly.

Final Answer:
4 : 1