Multiple choice

A certain distance between two villages is covered at a certain speed. If half of this distance is covered in double the time at new speed , then the ratio of the initial speed to the new speed is

  1. 2 : 1

  2. 1 : 2

  3. 4 : 1

  4. 1 : 4
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C Correct answer
Explanation

Let distance be D, initial speed be S1, new speed be S2. Time taken for D is T. Half distance D/2 is covered in 2T. So, D/2 = S2 * 2T. Since D = S1 * T, substitute: (S1 * T) / 2 = S2 * 2T. S1/2 = 2 * S2. S1/S2 = 4/1.

AI explanation

Let the total initial distance be D and the total initial time be T, making the initial speed equal to D/T. The new speed is calculated as (D/2) divided by (2*T), which simplifies to D/(4*T). The ratio of the initial speed (D/T) to the new speed (D/4T) is therefore 4:1.

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