Answer to Question #128525 in Classical Mechanics for Rimsha Ahmed

Question

Without any stoppage, a person travels a certain distance at an average speed of 42 km/h, and with stoppages, he covers the same distance at an average speed of 28 km/hr. How many minutes per hour does he stop?

14 minutes
15 minutes
28 minutes
None of these

Kindly, tell me how to solve this question, please.

Thank you.

Answer 1

What is the average speed? It is total distance over total time:

$$v=\frac{D}{t}.$$

Thus, for 42 km/h and no stops we have

$$42=\frac{D}{t_1}.$$

For 28 km/h it takes longer because certain time $t_s$ is required to stop:

$$28=\frac{D}{t_1+t_s}.$$

From the last equation:

$$t_s=\frac{D}{28}-t_1.$$

Substitute $t_1$expressed from the equation with 42 km/h:

$$t_s=\frac{D}{28}-\frac{D}{42}=\frac{D}{84}.$$

Compare this time with $t_1$:

$$t_1=\frac{D}{42},\\\space\\ \frac{t_s}{t_1}=\frac{1}{2},\\\space\\ t_s=0.5t_1.$$

Thus, stops last half of time that the traveler moves. They last 30 minutes per hour.