FOM Word Problem Drills: q33

[RyanS540]

p.393 in FOM (looking at digital copy)

The question states: If Roger took 2 hours to walk to a store that is 3 miles away, and then ran home along the same path in 1 hour, what was Roger's average speed, in miles per hour, for the round trip?

I did this by taking the average of the two rates. On the way to the store he was going 3 miles/2 hours, or 3/2 mph. On the way back he was going 3 miles/1 hour, 3 mph. The average of 3/2 and 3 is 2.25 mph.

The solution adds up the distance and total time to calculate the rate: (3 + 3) miles / (2 + 1) hours, which equals 2 mph.

I think both approaches should work but the answers are different. Am I making a careless error or what's going on? Thanks.

[Sage Pearce-Higgins]

You fell in the classic trap for this. The problem is, that he doesn't spend an equal time running and walking. If he did that, then, sure, his average speed would be halfway between his two speeds. This makes the problem more like a weighted average problem, and to solve it you have to calculate the total distance and divide it by the total time.