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
\(\frac{uw}{pw + qu}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
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 \(\frac{uw}{pw + qu}\)
= \(\frac{uw(p + q)}{pw + qu}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #60711)