Multiple choice

A boy walking at a speed of $10$ km/hr reaches his school $15$ minutes late. Next time he increases his speed by $2$ km/hr, but still, he is late by $5$ minutes. Find the distance of his school from his house.

  1. $10$ km
  2. $15$ km
  3. $20$ km
  4. $25$ km
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A Correct answer
Explanation

Let d be distance. Time = d/10. Late by 15 min means d/10 = T + 15/60. At 12 km/hr, d/12 = T + 5/60. Subtracting: d/10 - d/12 = 10/60 = 1/6. (6d - 5d)/60 = 1/6. d/60 = 1/6, so d = 10 km.

AI explanation

Using the constant distance formula, the distance equals the product of the two speeds multiplied by the difference in their time delays, all divided by the difference in the speeds. Substituting the speeds of 10 km/hr and 12 km/hr, and the time difference of 10 minutes (15 minus 5), gives (10 * 2 * 10/60) divided by 2. This solves to 200/60 divided by 2, making the distance 10 km.

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