Question

Sally travels by car from one city to another. She drives for 30.0 min at 80.0 km/hr, 12.0 min at 105.0 km/hr, and 45.0 min at 40.0 km/hr, and she spends 15.0 min eating lunch and buying gas.

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

Answer 1

To find the average speed of Sally's trip, we need to calculate the total distance traveled and the total time taken. The total distance traveled is 91.0 km and the total time taken is 1.70 hr. Therefore, the average speed is 53.53 km/hr.

Step-by-step explanation:

To find the average speed, we need to calculate the total distance traveled and the total time taken.

First, we calculate the distance traveled at each speed:

Distance at 80.0 km/hr: (30/60) * 80.0 = 40.0 km

Distance at 105.0 km/hr: (12/60) * 105.0 = 21.0 km

Distance at 40.0 km/hr: (45/60) * 40.0 = 30.0 km

The total distance traveled is 40.0 km + 21.0 km + 30.0 km = 91.0 km.

Next, we calculate the total time taken:

Time taken for driving: 30.0 min + 12.0 min + 45.0 min = 87.0 min = 1.45 hr

Time taken for lunch and gas: 15.0 min = 0.25 hr

The total time taken is 1.45 hr + 0.25 hr = 1.70 hr.

Finally, we calculate the average speed:

Average speed = Total distance traveled / Total time taken = 91.0 km / 1.70 hr = 53.53 km/hr.

Answer 2

A) The average speed for the trip is
`v_(average) =53,53(km)/(h)`.

B) The total distance traveled is
`d_(total)=91\ km`.

Step-by-step explanation:

Knowing that 1 hour has 60 minutes, we have that for each part of the trip:

`v_(1)=80(km)/(h)\ t_(1)=0,5\ h`

`v_(2)=105(km)/(h)\ t_(2)=0,2\ h`

`v_(3)=40(km)/(h)\ t_(3)=0,75\ h`

`v_(4)=0(km)/(h)\ t_(4)=0,25\ h`

Total distance traveled

The distance traveled is the speed multiplied by a period of time. The total distance traveled is calculated adding up the speeds multiplied by the given periods of time.

`d_(total)=d_(1)+d_(2)+d_(3)`

`d_(total)=v_(1).t_(1)+v_(2).t_(2)+v_(3).t_(3)`

`d_(total)=80(km)/(h).0,5\ h+105(km)/(h).0,2\ h+40(km)/(h).0,75\ h`

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

`d_(total)=91\ km`

B) The total distance traveled is
`d_(total)=91\ km`.

Average speed

The average speed could be calculated using the total distance traveled
`d_(total)` divided by the total time
`t_(total)`. We need to take into account the time spent eating lunch and buying gas.

`v_(average)=(d_(total))/(t_(total))`

`v_(average)=(v_(1).t_(1)+v_(2).t_(2)+v_(3).t_(3)+v_(4).t_(4))/(t_(1)+t_(2)+t_(3)+t_(4))`
`v_(average)=(91\ km)/(0,5\ h+0,2\ h+0,75\ h+0,25\ h)`

`v_(average)=(91\ km)/(1,70\ h)`

`v_(average)=53,53(km)/(h)`

A) The average speed for the trip is
`v_(average) =53,53(km)/(h)`.