Multiple choice

A cyclist cycles non-stop from $A$ to $B$ a distance of $14$ km at a certain average speed. If his average speed reduces by $1$ km/hr, then he takes $\displaystyle \frac{1}{3}$ hour more to cover the same distance. What was the original average speed of the cyclist?

  1. $3$ km/hr
  2. $5$ km/hr
  3. $7$ km/hr
  4. $11$ km/hr
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let v be the speed. We have 14/v - 14/(v-1) = -1/3. Solving this quadratic equation 14(v-1) - 14v = -v(v-1)/3 leads to v^2 - v - 42 = 0, which factors to (v-7)(v+6) = 0. Since speed must be positive, v = 7.

AI explanation

Let the original average speed of the cyclist be x km/hr, so the original time taken is 14/x hours. Using the formula Time = Distance / Speed for the reduced speed, the new time becomes 14/(x-1) hours. The problem states that the difference in time is 1/3 hour, giving the equation 14/(x-1) - 14/x = 1/3. Solving the resulting quadratic equation x^2 - x - 42 = 0 yields the original average speed as 7 km/hr.

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