Problem
Going there is 120 miles at 60 miles per hour, which takes 2 hours.
If you cover 60 miles each hour, 120 miles is just two of those hours - a simple division fact.
3.OA.A.3Identify SubproblemsComing home is 60 miles every 30 minutes, which is 120 miles per hour.
Two equal 30-minute halves make one hour, so the per-hour distance is double the per-half-hour distance.
4.MD.A.2Analyze The UnitsGoing home is 120 miles at 120 miles per hour, so it takes 1 hour.
Covering 120 miles in an hour means 120 miles takes exactly one hour.
3.OA.A.3Identify SubproblemsThe whole round trip is 120 + 120 = 240 miles, and the total time is 2 + 1 = 3 hours. Average speed is total distance divided by total time.
Average speed asks 'how many miles per hour overall,' so divide all the miles by all the hours.
4.MD.A.2Analyze The UnitsThe average speed for the whole round trip is the total distance divided by the total time.
Average speed means the single unchanging speed that would carry you over the same whole trip in the same whole time, so we ask what steady speed fits all the miles into all the hours.
At a steady speed the distance equals the speed times the number of hours, so to recover the speed we divide the distance by the hours.
A steady speed in miles per hour is the same batch of miles added on in every hour, so many hours pile up that many equal groups of miles.
Building the distance by multiplying and recovering the speed by dividing are opposite moves that undo each other.
We divide the total distance and the total time because the round trip is exactly its two legs joined with no gap and no overlap, so all the miles are the legs' miles added together and all the hours are the legs' hours added together.
Pieces that fit together with no gap and no overlap add back up to the whole thing.
Average speed is all the miles divided by all the hours - not just the average of the two speeds!