Multiple choice

Walking $\displaystyle \dfrac{6}{7}$th of his usual speed a man is $12$ minutes late. The usual time taken by him to cover that distance is:

  1. $1$ hour
  2. $1$ hr $12$ min
  3. $1$ hr $15$ min
  4. $1$ hr $20$ min
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the usual speed be v and usual time be t. Distance = vt. New speed = (6/7)v, new time = t + 12. Since distance is constant, vt = (6/7)v(t + 12). Dividing by v, t = (6/7)t + 72/7. (1/7)t = 72/7, so t = 72 minutes, which is 1 hour 12 minutes.

AI explanation

Using the constant distance formula Speed * Time = Distance, if his new speed is 6/7 of his usual speed, his new time becomes 7/6 of his usual time. The difference between the new time and the usual time is 7/6 T - T = 1/6 T. This difference is given as 12 minutes, so 1/6 T = 12, which means T = 72 minutes. Therefore, his usual time is 1 hr 12 min.

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