Question

we drive a distance of 1km at 16km/hr. Then we drive am additional distance of 1 km at 32 km/hr. what ia our average speed?

Answer 1

We can find the average speed from the formula:

$$v_{avg}=\dfrac{Total\ distance}{Total\ time\ elapsed}.$$

The total distance traveled is the sum of two distances: the initial distance $s_1$ and the additional distance $s_2$. Therefore, we can write:

$$Total\ distance=s_1+s_2=1\ km+1\ km=2\ km.$$

The total time elapsed is the sum of two times: the time $t_1$that the car takes to travel the distance $s_1$and the time $t_2$ that the car takes to travel the additional distance $s_2$.

Therefore, we can write:

$$Total\ time\ elapsed=t_1+t_2=\dfrac{s_1}{v_1}+\dfrac{s_2}{v_2},$$ $$Total\ time\ elapsed=\dfrac{1\ km}{16\ \dfrac{km}{hr}}+\dfrac{1\ km}{32\ \dfrac{km}{hr}}=0.094\ hr.$$

Finally, we can find the average speed:

$$v_{avg}=\dfrac{Total\ distance}{Total\ time\ elapsed}=\dfrac{2\ km}{0.094\ hr}=21.3\ \dfrac{km}{hr}.$$

Answer:

$v_{avg}=21.3\ \dfrac{km}{hr}.$