Question

a person goes to his friends home at the speed of 30 km/h and comes back at the speed of 40 km/h. what was his average speed throughout the entire trip?

Answer 1

Let $d$ be the distance between the two houses. Considering the formula

$d=vt$

where $d$ is the distance, $v$ is the velocity and $t$ is the time, we can solve it for the time to get

$t=\dfrac{d}{v}$

So, the two trips take the following time:

$t_1 = \dfrac{d}{30},\quad t_2=\dfrac{d}{40}$

To get the average speed, we need to consider the two trips together. Globally, the person traveled a distance of $2d$, and the global time is the sum of the two times. We have

$v=\dfrac{d_{TOT}}{t_{TOT}}=\dfrac{2d}{\frac{d}{30}+\frac{d}{40}}=\dfrac{2}{\frac{1}{30}+\frac{1}{40}}=\dfrac{2}{\frac{7}{120}}=\dfrac{240}{7}$