Answer to Question #141472 in Physics for Elizabeth

Question

A motorist travels 160km at 80km/h and 160km at 100km/h. What is the average speed of the motorist for this trip?

Answer 1

We can find the average speed of the motorist for this trip from the formula:

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

The total distance traveled is the sum of two distances: the distance $s_1$ traveled at a speed 80 km/h  and the distance $s_2$ traveled at a speed 100 km/h. Therefore, we can write:

$$Total\ distance=s_1+s_2=160\ km+160\ km=320\ km.$$

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

Therefore, we can write:

$$Total\ time\ elapsed=t_1+t_2=\dfrac{s_1}{v_1}+\dfrac{s_2}{v_2},$$ $$Total\ time\ elapsed=\dfrac{160\ km}{80\ \dfrac{km}{h}}+\dfrac{160\ km}{100\ \dfrac{km}{h}}=3.6\ h.$$

Finally, we can find the average speed of the motorist for this trip:

$$v_{avg}=\dfrac{Total\ distance}{Total\ time\ elapsed}=\dfrac{320\ km}{3.6\ h}=89 \ \dfrac{km}{h}.$$

Answer:

$v_{avg}=89 \ \dfrac{km}{h}.$