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

Algebra ->  Customizable Word Problem Solvers  -> Travel -> 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      Log On

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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) About Me  (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 %2850+%2B+40%29%2F2+=+45, 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: d+=+rt 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.
%28d1+%2B+d2%29%2F%28t1+%2B+t2%29
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 d+=+rt or t+=+d%2Fr
t1+=+d1%2Fr1
t1+=+x%2F50
t1+=+0.02x
----------------
t2+=+d2%2Fr2
t2+=+x%2F40
t2+=+0.025x
Now we can find the weighted average speed (M) for the round-trip.
M+=+%28d1%2Bd2%29%2F%28t1%2Bt2%29
M+=+%28x%2Bx%29%2F%280.02x%2B0.025x%29
M+=+2x%2F0.045x Cancel the x's
M+=+2%2F0.045
m+=+44.4
The aveage speed for the trip is 44.4 mph