Multiple choice

A man covers a distance of $25$ km in an hour, partly on foot at the rate of $4$ km/hr and partly on motorcycle at $32$ km/hr. Find the distance travelled on the motorcycle.

  1. $14$km
  2. $32$km
  3. $24$km
  4. $9$km
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C Correct answer
Explanation

Let x be distance on foot, y on motorcycle. x + y = 25. x/4 + y/32 = 1. Multiply by 32: 8x + y = 32. Subtract x+y=25: 7x = 7, x = 1. Then y = 24 km.

AI explanation

Let the time travelled on the motorcycle be t hours, making the time on foot (1 minus t) hours. The total distance is the sum of the distances on foot and motorcycle, giving 4(1 minus t) plus 32t equals 25. Solving this equation, 4 plus 28t equals 25, so 28t equals 21 and t equals 3/4 hours. The distance on the motorcycle is the speed multiplied by the time, which is 32 multiplied by 3/4, equalling 24 km.

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