Multiple choice

I started on my bicycle at $7$ A.M. to reach a certain place. After going a certain distance, my bicycle went out of order. Consequently, I rested for $35$ minutes and came back to my house walking all the way. I reached my house at $1$ P.M. If my cycling speed is $10$ km/hr and my walking speed is $1$ km/hr, then what distance did I cover on my bicycle?

  1. $\displaystyle 3\frac{61}{66}$ km
  2. $\displaystyle 4\frac{61}{66}$ km
  3. $\displaystyle 6\frac{61}{66}$ km
  4. $\displaystyle 7\frac{61}{66}$ km
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let distance be D. Cycling time = D/10. Walking time = D/1. Total time = 6 hours (7 AM to 1 PM). Total time = D/10 + D/1 + 35/60 = 6. 11D/10 = 6 - 7/12 = 65/12. D = 65/12 * 10/11 = 650/132 = 325/66 = 4 61/66 km.

AI explanation

The total time spent away from home is 6 hours, from 7 A.M. to 1 P.M. Subtracting the 35-minute rest period leaves 5 and 5/12 hours of total travel time. Let d be the distance cycled at 10 km/hr and walked back at 1 km/hr, so the travel time equation is d/10 + d/1 = 65/12. Multiplying the entire equation by 10 gives 11d = 650/12, so the distance cycled is 4 and 61/66 km.

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