A car travels from calabar to Enugu, a distance of P km with an average speed of U km per hour and continues…

Analyze the question: The car makes two legs of a journey at different speeds. We want the average speed for the whole trip.

Concept: Average speed = total distance ÷ total time. It is not the simple average of the two speeds unless the times are equal.

Solution:

1. Total distance = P + Q

2. Time for the first leg (Calabar to Enugu): t₁ = distance ÷ speed = P/U

3. Time for the second leg (Enugu to Benin): t₂ = Q/W

4. Total time: t = P/U + Q/W = (PW + QU)/(UW)

5. Average speed:

Average speed = (P + Q) ÷ [(PW + QU)/(UW)]

= (P + Q) × UW/(PW + QU)

= UW(P + Q)/(PW + QU)

This matches option B. It also passes a quick check: if U = W, it should reduce to U. Then UW(P + Q)/(PW + QU) = U²(P + Q)/(U(P + Q)) = U, which is correct.

Correct answer: B

Tip: For average speed questions, always find total distance and total time separately, then divide. When you divide by a fraction like (PW + QU)/(UW), flip it and multiply. Option A fails a units check, since it doesn't give km/h. Use a quick check like setting U = W to eliminate wrong options.