Question

Sally travels by car from one city to another. She drives for 30 min at 80 km/hr, 12 min at 105 km/hr, and 45 min at 40 km/hr, and she spends 15 min eating lunch and buying gas.

A. Determine the average speed for the trip.
B. Determine the total distance traveled.

Answer 1

A. 53.5 km/h B. 91.0 km/h

Answer 2

The average speed is 91km/hr and the total distance traveled is 91km.

Step-by-step explanation:

The average speed can be defined as the quotient between the total distance traveled and the time that took.

By given, we have the speed of each interval, and their corresponding time, we just need to find the distance traveled in each interval, and sum them all

`t=30min; v=80km/hr`

First, we need to transform minutes to hours. We know that 1 hour equals 60 minutes.

Interval 1.

`t=30min(1hr)/(60min)=(1)/(2)hr`

Then, we use the definition of constant movements, assuming that's an actual constant motion

`d=st\\d=80km/h((1)/(2)hr )\\d=40km`

Now, we do the same for the rest of the intervals

Interval 2.

`t=12min: v=105km/hr`

`t=12min(1hr)/(60min)=(1)/(5) hr`

Then,

`d=vt\\d=105km/hr((1)/(5)hr )\\d=21km`

Interval 3.

`t=45min;v=40km/hr`

`t=45min(1hr)/(60min)= (9)/(12)hr=(3)/(4)hr`

`d=vt\\d=40km/hr((3)/(4) hr)\\d=30km`

So, the total distance traveled is

`d_(total)=40km+21km+30km= 91km`

And the total time is

`t_(total)=(1)/(2)hr+(1)/(5)hr+(3)/(4) hr= (10+4+15)/(20) hr=(29)/(20)hr = 1.45hr`

Now, the average speed is

`v=(d_(total) )/(t_(total) )=(91km)/((29)/(20)hr )=(1820km)/(20hr)=91km/hr`

Therefore, the average speed is 91km/hr and the total distance traveled is 91km.