A car travels from calabar to Enugu, a distance of P km with an average...

JAMB 1991

A car travels from calabar to Enugu, a distance of P km with an average speed of U km per hour and continues to benin, a distance of Q km, with an average speed of Wkm per hour. Find its average speed from Calabar to Benin

A. \(\frac{(p + q)}{pw + qu}\)
B. \(\frac{uw(p + q)}{pw + qu}\)
C. \(\frac{uw(p + q)}{pw}\)
D. \(\frac{uw}{pw + qu}\)

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Correct Answer: Option B

Explanation

Average speed = \(\frac{total Distance}{Total Time}\)

from Calabar to Enugu in time t1, hence

t1 = \(\frac{P}{U}\) also from Enugu to Benin

t2 \(\frac{q}{w}\)

Av. speed = \(\frac{p + q}{t_1 + t_2}

= p + q * \frac{p}{u} + \frac{q}{w}\)

= p + q x \(\frac{uw}{pw + qu}\)

= \(\frac{uw(p + q)}{pw + qu}\)