Answer:
Approximately [tex]43.2[/tex] kilometers per hour.
Explanation:
To find average speed, divide the total distance travelled by the total duration of the motion:
[tex]\displaystyle (\text{average speed}) = \frac{(\text{total distance})}{(\text{total duration})}[/tex].
In this question, while the exact distance between the towns is not given, the ratio between the two distances is known. Let [tex]s[/tex] denote the distance (in kilometers, where [tex]s > 0[/tex]) between [tex]\sf P[/tex] and [tex]\sf Q[/tex]:
To find the average speed, the total duration of the journey also needs to be found. To find total duration, start by finding the time required to cover each part of the journey:
Hence, the total duration of the motion would be [tex]((s / 36) + (s / 48))[/tex] hours.
Divide the total distance travelled by the total duration to find average speed:
[tex]\begin{aligned} & (\text{average speed}) \\ =\; & \frac{(\text{total distance})}{(\text{total duration})} \\ =\; & \frac{s + 2\, s}{\displaystyle \frac{s}{36} + \frac{2\, s}{48}} \\ =\; & \frac{1 + 2}{\displaystyle \frac{1}{36} + \frac{2}{48}} && (\text{$s$ is eliminated}) \\ =\; & \frac{216}{5}\end{aligned}[/tex].
In other words, the average velocity of this journey would be [tex](216 / 5)[/tex] kilometers per hour, which is approximately [tex]43.2[/tex] kilometers per hour.