Question 28163
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 {{{(50 + 40)/2 = 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. 
{{{(d1 + d2)/(t1 + t2)}}}
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/r}}}
{{{t1 = d1/r1}}}
{{{t1 = x/50}}}
{{{t1 = 0.02x}}}
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{{{t2 = d2/r2}}}
{{{t2 = x/40}}}
{{{t2 = 0.025x}}}

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

{{{M = (d1+d2)/(t1+t2)}}}
{{{M = (x+x)/(0.02x+0.025x)}}}
{{{M = 2x/0.045x}}} Cancel the x's
{{{M = 2/0.045}}}
{{{m = 44.4}}}

The aveage speed for the trip is 44.4 mph