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A boy is walking at a speed of P km/h to cover a distance of 1 km. However, due to slippery ground, his speed decreases by Q km/h (P > Q). If he takes R hours to cover the distance, then find the relation between R and Q.

A boy is walking at a speed of P km/h to cover a distance of 1 km. However, due to slippery ground, his speed decreases by Q km/h (P > Q). If he takes R hours to cover the distance, then find the relation between R and Q. Correct Answer 1/R = P - Q

Given:

Initial speed = P km/h,

Decreased by Q km/h,

Distance covered = 1 km.

Time taken = R hours.

Concept used:

Distance = Speed × Time

Calculation:

So, the actual speed of the boy = (P - Q) km/h

According to the question,

(P - Q) × R = 1

⇒ 1/R = (P - Q)

∴ The relation between R and Q is 1/R = (P - Q).

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