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?
Aptitude
Time and Distance
Difficulty: Easy
Choose an option
Answer
Correct Answer: 4 : 1
Explanation
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:
v2 = (D/2) / (2T) = D / (4T) = v1 / 4So v1 : v2 = 4 : 1Verification / 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