Multiple choice

A boy is running at a speed of $p$ km/hr to cover a distance of $1$ km. But, due to slippery ground, his speed is reduced by $q$ km/hr $(p > q).$ If he takes $r$ hours to cover the distance, then,

  1. $\displaystyle \frac{1}{r} = (p - q)$
  2. $r = (p - q)$
  3. $\displaystyle \frac{1}{r} = (p + q)$
  4. $r = (p + q)$
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A Correct answer
Explanation

Time = Distance / Speed. The distance is 1 km. The reduced speed is (p - q) km/hr. The time taken is r hours. Therefore, r = 1 / (p - q), which implies 1/r = p - q.

AI explanation

Using the formula time equals distance divided by speed, the new effective speed of the boy is (p - q) km/hr. Since the distance is 1 km, the time taken r is equal to 1 divided by (p - q). Rearranging this relationship gives 1/r = (p - q).

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