Question

. A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 30.0 min at 80.0 km/h, 12.0 min at 100 km/h, and 45.0 min at 40.0 km/h and spends 15.0 min eating lunch and buying gas. (a) Determine the average speed for the trip. (b) Determine the distance between the initial and final cities along the route.

Answer 1

Answer:

a) The average speed for the trip is 52.9 $\frac{km}{hr}$

b) The distance between the initial and final cities along the route is 90 km.

Explanation:

First, knowing that 1 hour is 60 minutes, the conversion of the times in which you travel at each speed or for lunch or buy gas is performed:

• 30 minutes: 0.5 hr
• 12 minutes: 0.2 hr
• 45 minutes: 0.75 hr
• 15 minutes: 0.25 hr

Velocity ​​is a physical quantity that expresses the relationship between the space traveled by an object in the following way:

$Velocity=\frac{change of position}{time}$

Then:

change of position=velocity*time

So, in this case:

• change of position 1= 0.5 hr* 80 $\frac{km}{hr}$= 40 km

• change of position 1= 0.2 hr* 100 $\frac{km}{hr}$= 20 km

• change of position 1= 0.75 hr* 40 $\frac{km}{hr}$= 30 km

So, the total distance traveled is change of position 1+ change of position 2 + change of position 3= 40 km + 20 km + 30 km= 90 km

And the total elapsed time is considering the lunch time and gas purchase added to the time to make the journey to the technical stop: 0.5 hr + 0.2 hr + 0.75 hr + 0.25 hr= 1.7 hr

So, the velocity is:

$Velocity=\frac{90 km}{1.7 hr}$

$Velocity=52.9 \frac{km}{hr}$

Finally:

a) The average speed for the trip is 52.9 $\frac{km}{hr}$

b) The distance between the initial and final cities along the route is 90 km.

Answer 2

Total distance covered = 40+20+30 = 90 km

Total time taken to cover this distance = .5 hr + .2 hr + .75 hr = 1.75 hr

Avg. speed of Trip would be 
90/1.45 = 62.07 km