Question

A person travels by car from one city to another with different constant speeds between pairs of cities. She drive 60.0 min at 100.0km/h, 5.0 min at 90.0 km/h, and 40.0 min at 60.0km/h and soends 30.0 min eating lunch and buying gas. (A) determine the average speed for the trip. (B) determine the distance between the intial and final cities alkng the route

Answer 1

The average speed for the trip is 65.56
`(km)/(h)` and the distance between the intial and final cities along the route is 147.5 km

Step-by-step explanation:

You know:

• t1= 60.0 min= 1 h
• v1= 100.0km/h
• t2= 5.0 min= 1/12 h
• v2= 90.0 km/h
• t3= 40.0 min= 2/3 h
• v3= 60.0km/h
• t4=30.0 min= 0.5 h= 1/2 h
• v4= 0 because she stops to eat lunch and buy gas.

Speed is a quantity that reflects the space traveled by a body in a unit of time. That is, the average velocity relates the change in position with the time taken to effect said change.

`speed=(change in position)/(time)`

To calculate the average speed of the trip you must calculate the total distance traveled and the total time used.

The total time used for the trip is:

t= t1 + t2 + t3 + t4= 60 min + 5 min + 40 min + 30 min= 135 min= 2.25 h

The distance traveled in each stage of the trip is calculated knowing the speed in that stage and the time used by the expression:

distance= speed*time

Then:

• distance1= v1*t1 = 100 km/h * 1 h= 100 km
• distance2= v2*t2 = 90 km/h * 1/12 h= 7.5 km
• distance3= v3*t3 = 60 km/h * 2/3 h= 40 km
• distance4= v4*t4 = 0 km/h * 1/2 h= 0 km

So, the total distance traveled is calculated as:

d= 100 km + 7.5 km + 40 km + 0 km= 147.5 km

Then, the average speed for the trip is:

`average speed=(total distance)/(total time)`

`average speed=(147.5 km)/(2.25 h)`

average speed= 65.56
`(km)/(h)`

The average speed for the trip is 65.56
`(km)/(h)` and the distance between the intial and final cities along the route is 147.5 km