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

$\frac{1}{r}=p-q$

The correct answer is Option (1) → $\frac{1}{r}=p-q$

To determine the relationship between the speed, distance, and time in this scenario, we can use the fundamental formula of motion:

$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$

Step 1: Identify the Variables

• Original Speed: $p \text{ km/hr}$
• Reduction in Speed: $q \text{ km/hr}$
• Actual (Reduced) Speed: Since the speed is reduced by $q$, the effective speed is $(p - q) \text{ km/hr}$.
• Distance Covered: $1 \text{ km}$
• Time Taken: $r \text{ hours}$

Step 2: Apply the Formula

Substitute the actual speed, distance, and time into the formula:

$p - q = \frac{1}{r}$

Alternatively, rearranging for $1$:

$1 = (p - q) \times r$