Comparing speeds from distance–time change A distance D is covered at speed v1 in time T. If half the distance (D/2) is covered in double the time (2T), what is the ratio v1 : v2 of the two speeds?

Introduction / Context:
Speed equals distance divided by time. Changing distance and time scales the speed accordingly. Here, the second scenario uses half the distance but takes double the time versus the original benchmark.

Given Data / Assumptions:

• Original: distance D in time T ⇒ v1 = D / T.
• New: distance D/2 in time 2T ⇒ v2 = (D/2) / (2T).

Concept / Approach:
Compute v2 relative to v1 by simplifying the fraction. Then form the ratio v1 : v2 and reduce to simplest integers.

Step-by-Step Solution:

Verification / Alternative check:
Choose D = 4 and T = 1. Then v1 = 4, v2 = (2)/(2) = 1 ⇒ 4:1.

Why Other Options Are Wrong:
2:1 or 1:2 would occur under different scalings; here both distance and time changed.

Common Pitfalls:
Dividing 1/2 by 2 and incorrectly getting 1 instead of 1/4 for the speed factor.

Final Answer:
4 : 1