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.

\(\frac{uw}{pw + qu}\)

Correct answer is B

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 = \(\frac{p + q}{t_1 + t_2}\)

= \(\frac{p + q}{p/u + q/w}\)

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

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