A certain distance is covered at speed v1. If half of this distance is covered in double the original time, what is the ratio of the two speeds (v1 : v2)?

Introduction / Context: Speed is distance divided by time. Comparing two scenarios for the same benchmark distance allows a direct speed-ratio calculation.

Given Data / Assumptions: Let original distance be D in time T at speed v1. New scenario covers D/2 in time 2T at speed v2.

Concept / Approach: Compute v1 and v2 symbolically and then take the ratio v1 : v2.

Step-by-Step Solution: v1 = D / T. v2 = (D/2) / (2T) = D / (4T) = v1 / 4. Thus v1 : v2 = (v1) : (v1/4) = 4 : 1.

Verification / Alternative check: Choose D = 100 and T = 10 ⇒ v1 = 10. New: 50 in 20 ⇒ v2 = 2.5 ⇒ v1 : v2 = 10 : 2.5 = 4 : 1.

Why Other Options Are Wrong: 1 : 4, 2 : 1, 1 : 2, 3 : 1 contradict v2 = v1/4.

Common Pitfalls: Misreading “half of the distance in double the time” and inverting the ratio.

Final Answer: 4 : 1