Julie drives 100 mi to Grandmother's house. on the way to grandmothers h's Julie drives half the distance at 40 mph and half the distance at 60 mph. On her return trip, she drives half the time at 40 mph and half the time at 60 mph.

a) what is Julie's average speed on the way to grandmother's house?

b) what is her average speed in the return trip?

a) On the way to Grandmother's the average velocity is 48 mi/h.

b) In the return trip, the average velocity is 50 mi/h

Explanation:

Hi there!

The average velocity (AV) is calculated as follows:

AV = Δx / Δt

Where:

Δx = traveled distance = final position - initial position

Δt = elapsed time

a) Let's find the time it takes Julie to travel 50 mi (half the total distance) at 60 and 40 mph:

At 60 mph:

60 mi/h = 50 mi / Δt

Δt = 50 mi / 60 mi/h = 5/6 h

At 40 mph:

40 mi/h = 50 mi / Δt

Δt = 50 mi / 40 mi/h = 1.25 h

The total time of travel is 1.25 h + 5/6 h = 25/12 h

Then, the AV will be:

AV = 100 mi / 25/12 h = 48 mi/h

On the way to Grandmother's the average velocity is 48 mi/h.

b) Now let's calculate the AV on the return trip. During the first half of the trip, the elapsed time is half of the total time (Δt/2) and the traveled distance is unknown, Δx1.

Then, the average velocity during the first half of the trip can be written as follows.:

40 mi/h = Δx1 / (1/2 Δt)

Solving for Δx1:

20 mi/h · Δt = Δx1

During the second half of the trip the average velocity will be:

60 mi/h = Δx2 / (1/2 Δt)

Solving for Δx2:

30 mi/h · Δt = Δx2

The average velocity for the entire trip can be expressed as follows:

AV = Δx / Δt

Δx = Δx1 + Δx2 = 20 mi/h · Δt + 30 mi/h · Δt = 50 mi/h · Δt

Then:

AV = 50 mi/h · Δt / Δt = 50 mi/h

In the return trip, the average velocity is 50 mi/h