SOLUTION: Jackie dives x distance at 50 miles per hour and returns over the same route at 40 miles per hour. What is her average speed for the round trip in miles per hour? A. 40.3 B. 44.4

Question 28163: Jackie dives x distance at 50 miles per hour and returns over the same route at 40 miles per hour. What is her average speed for the round trip in miles per hour?
A. 40.3
B. 44.4
C. 45.0
D. 46.2
E. 47.5
I thought that when you figure the average in a problem you add up all the numbers and then divide by the amount of numbers there are. I believe that the answer should be (C). The answer they say is (B). Why?
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
To solve this problem, you will need to find "weighted average" speed.
While it does seem that the average speed for Jackie's round trip ought to be , Jackie did not drive at the given speeds for equal amounts of time, so you must find the weighted average speed for the trip.
Using the formula: where: d = distance traveled, r = rate of travel (speed), and t = the time taken to travel the distance, d, you can find the weighted average speed by dividing the sum of the distances for each leg by the sum of the times taken for each leg.

The distance for each leg is given as x, so the sum for the trip is 2x.
The times for each leg are not given so they must be calculated. Using or

----------------

Now we can find the weighted average speed (M) for the round-trip.

Cancel the x's

The aveage speed for the trip is 44.4 mph

RELATED QUESTIONS
A man travels a distance of 20 miles at 60 miles per hour and then returns over the same... (answered by stanbon)

A man travels a certain distance at 60 miles per hour and returns over the same road at... (answered by Alan3354)

A cyclist bikes x distance at 10 miles per hour and returns over the same path at 8 miles (answered by ikdeep)

A cyclist bikes x distance at 10 miles per hour and returns over the same path at 8... (answered by Alan3354)

A cyclist bikes x distance at 10 miles per hour and returns over the same path at 8... (answered by stanbon)

Sam drove to work at an average speed of 50 miles per hour from her house and then... (answered by Alan3354)

Danielle drives from her home to the store at an average speed of 40 miles per hour. She... (answered by amoresroy)

a motorcyclist travels 90 miles at rate of 20 miles per hour, if he returns same distance (answered by mananth)

A truck driver travels a certain distance at 60 miles per hour and returns over the same... (answered by Edwin McCravy)