Question

A boy is running at a speed of p km/h to cover a distance of 1 km but due to slippery ground his speed is reduced by q km/h \((p > q).\) If he takes r hours to cover the distance, which of the following condition is true:

• A. \(\frac{1}{r}=(p-q)\)
• B. r=(p-q)
• C. \(r=\frac{1}{p+q}\)
• D. r=p+q

Answer 1

The Correct Option is A

To solve this problem, we need to determine the relationship between the variables given: the boy's speed before reduction (p km/h), the reduction in speed due to slippery ground (q km/h), and the time taken to cover the distance (r hours).

The boy's effective speed after reduction is (p - q) km/h. Given that the boy covers a distance of 1 km, we can use the formula:

Time = Distance / Speed

Substituting the given values into this equation, we have:

r = 1 / (p - q)

Rearranging the equation, we get:

1 / r = (p - q)

Thus, the correct condition is that the reciprocal of the time taken is equal to the effective speed after reduction, which matches the option:

\(\frac{1}{r}=(p-q)\)