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 s...

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 w km per hour. Find its average speed from Calabar to Benin

Answer Details

Average speed = $\frac{\text{total Distance}}{\text{Total Time}}$
from Calabar to Enugu in time t1, hence
t1 = $\frac{p}{u}$ also from Enugu to Benin
t2 = $\frac{q}{w}$
Average speed = $\frac{p+q}{t_1+t_2}$
= $\frac{p+q}{\frac{p}{u}+\frac{q}{w}}$
= p + q × $\frac{uw}{pw+qu}$
= $\frac{uw(p+q)}{pw+qu}$