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Answer to this question is NOT straight forward as taking average of speeds. People often make mistakes. Such an average is correct only when I travel for equal durations of time.

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Let us assume I travelled from A to B, a distance of S miles at 20 mph and then returned back to A at 30 mph.

Average speed = total distance travelled / total time duration.

So we have to find the quantities on the RHS.

Time taken to go from A to B = S / 20 hours

Time taken to return from B to A = S / 30 hours

total time = S [ 1/20 + 1/30 ] = 5 S/60 = S/12 hours

Average speed = (S+S) / (S/12) = 24 mph

=============================

Let us assume I travelled from A to B, a distance of S miles at 20 mph and then returned back to A at 30 mph.

Average speed = total distance travelled / total time duration.

So we have to find the quantities on the RHS.

Time taken to go from A to B = S / 20 hours

Time taken to return from B to A = S / 30 hours

total time = S [ 1/20 + 1/30 ] = 5 S/60 = S/12 hours

Average speed = (S+S) / (S/12) = 24 mph