Question

A person takes a trip, driving with a constant speed of 99.5 km/h, except for a 22.0-min rest stop. If the person's average speed is 73.4 km/h, find the following.

(a) How much time is spent on the trip?

(b) How far does the person travel?

Answer 1

a) By the definition of the average speed, we have:

$$v_{avg}=\dfrac{d}{t_{tot}},$$

here, $v_{avg}$ is the person's average speed, $d$ is the total distance covered by the person, $t_{tot}$ is total time spent on the trip.

Then, from this equation, we can find $t_{tot}$:

$$t_{tot}=\dfrac{d}{v_{avg}}.$$

We can find $d$ from the formula:

$$d=vt,$$

here, $v$ is the constant speed of the person.

The total time for the entire trip can be found as follows:

$$t_{tot}=t+t_{rest},$$

here, $t_{rest}$ is the rest stop time.

Then, we get:

$$t+t_{rest}=\dfrac{vt}{v_{avg}},$$ $$t=\dfrac{t_{rest}}{\dfrac{v}{v_{avg}}-1},$$ $$t=\dfrac{22\ min\cdot\dfrac{1\ h}{60\ min}}{\dfrac{99.5\ \dfrac{km}{h}}{73.4\ \dfrac{km}{h}}-1}=1.03\ h.$$

Finally, we can find total time spent on the trip:

$$t_{tot}=t+t_{rest}=1.03\ h+22\ min\cdot\dfrac{1\ h}{60\ min}=1.4\ h.$$

b) Then, we can find the total distance covered by the person:

$$d=vt=99.5\ \dfrac{km}{h}\cdot1.03\ h=102.5\ km.$$