Multiple choice

A started on my bicycle at $7$ $a.m.$ to reach a certain place. After going a certain distance his bicycle went out of order. Consequently, A rested for $35$ minutes and came back to his house walking all the way A reached my house at $1$ $p.m.$ If his cycling speed is $10$ $kmph$ and his walking speed is $1$ $kmph$, then on his bicycle A covered a distance of :

  1. $\displaystyle 4\frac{61}{66}$ $km$
  2. $\displaystyle 13\frac{4}{9}$ $km$
  3. $\displaystyle 14\frac{3}{8}$ $km$
  4. $\displaystyle 15\frac{10}{21}$ $km$
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A Correct answer
Explanation

Let d be the distance cycled. Time cycling = d/10. Time walking = d/1. Total time = 6 hours - 35 mins rest = 5 hours 25 mins = 325/60 hours = 65/12 hours. d/10 + d/1 = 65/12 => 11d/10 = 65/12 => d = 650/132 = 325/66 = 4 and 61/66 km.

AI explanation

The total time away from home is from 7 a.m. to 1 p.m., which is 6 hours. Subtracting the 35 minutes of rest leaves 5 hours and 25 minutes of travel time. Setting up the equation where the forward distance x divided by 10 plus the return distance x divided by 1 equals 325/60 hours gives 11x equals 325/6. Solving for x yields a distance of 4 and 61/66 kilometers.

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