Question

Julie drives 100 mi to Grandmother's house. On the way to Grandmother's, Julie drives half the distance at 39.0 mph and half the distance at 61.0 mph . On her return trip, she drives half the time at 39.0 mph and half the time at 61.0 mph . You may want to review (Pages 33 - 36) . Part A What is Julie's average speed on the way to Grandmother's house? Express your answer with the appropriate units.

Answer 1

The average speed is 47.62 mph.

Why?

To calculate the average speed of Julie, we need to calculate the time taken to cover the first 50 miles (at 39 mph) and then, the other 50 miles (at 61 mph).

So, calculating we have:

- Traveling at 39 mph, first 50 miles:

We have that:

`speed=(distance)/(time)`

`distance=speed*time\\\\time=(distance)/(speed)`

Now, substituting the given information, we have:

`time_(1)=(50miles)/(39(miles)/(hour))\\\\time_(1)=1.28hour`

So, we know thay Julie traveled the first 50 miles in 1.28 hours.

- Traveling at 61 mph, last 50 miles:

Substituting the given information, we have:

`time_(2)=(50miles)/(61(miles)/(hour))\\\\time_(2)=0.82hour`

So, we know thay Julie traveled the last 50 miles in 0.82 hours.

Then, if we need to calculate the average speed, we can use the following formula:

`AverageSpeed=(TotalDistance)/(TotalTime)`

We can rewrite the formula, to make it fit with our problem, we have:

`AverageSpeed=(TotalDistance)/(t_(1)+t_(2))`

Finally, substituting the obtained values for the times, we have:

`AverageSpeed=(100miles)/(1.28hours+0.82hour)`

`AverageSpeed=(100miles)/(2.1hours)`

`AverageSpeed=(100miles)/(2.1hours)=47.62mph`

Hence, we have that the average speed of Julie on the way to Grandmother's house is 47.62 mph.

Have a nice day!