Multiple choice

A certain distance is covered at a certain speed (s1). If half of this distance is covered in double the time at speed (s2). Find the ratio of the two speeds. Also, if s1 is 60 km/hr, then find s2.

  1. 1 : 16, 3.75 km/hr

  2. 4 : 1, 15 km/hr

  3. 2 : 1, 30 km/hr

  4. 2 : 8, 240 km/hr
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B Correct answer
Explanation

Distance D at speed s1 takes time t = D/s1. Half distance D/2 at speed s2 takes time 2t. So s2 = (D/2) / (2t) = D / (4t) = (D/t) / 4 = s1 / 4. Thus s1/s2 = 4/1. If s1 = 60, s2 = 15.

AI explanation

Let the original distance be d and the original time be t, so the first speed s1 is d divided by t. The second scenario covers half the distance in double the time, meaning the distance is d/2 and the time is 2t. The second speed s2 equals (d/2) divided by 2t, which simplifies to d divided by 4t. Comparing s1 and s2, the ratio is 4:1, and if s1 is 60 km/hr, then s2 is 60 divided by 4, which is 15 km/hr.

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