Average speed of a round trip
You drive to a town at 60 miles per hour and come back along the same road at 30 miles per hour. What is your average speed for the whole round trip, in miles per hour?
Fractions, decimals with at least 3 significant digits, and expressions such as sqrt(2)/2, e^-1 or pi/4.
Average speed is total distance divided by total time. Pick a convenient distance.
Say the town is 60 miles away.
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s Shown after a correct answer. Revealing it first marks the problem as seen, not solved.
Idea. Average speed is total distance over total time. The slow leg takes longer, so it counts for more of the time, and the average is below the midpoint of 45.
Step 1. Say the town is miles away. Going takes hours and coming back hours: hours in all.
Step 2.
The trap. Answering 45, the average of the two speeds. The right average is the harmonic mean, .
A follow-up. If you drive the first half of the distance at 30 mph, no speed on the way back can give an average of 60 mph: at 60 mph overall, the whole trip would take exactly as long as the first half already took.