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Mathematical Reasoning Puzzles - Solution for #7

Solution for #7

Let d be the distance to the store, T be the time it gets to get there, t be the time it takes to get back, and A be the average speed (which is what we want to find out). As we know from elementary mathematics, distance equals rate times time:

      d = 20T
T = d/20

d = 30t
t = d/30

Now that we have expressions for T and t, we can come up with an equation that describes the round trip:

     2d = A(T + t)
2d = A(d/20 + d/30)
2d = A(3d/60 + 2d/60)
2d = A(5d/60)
A = 120d/5d
A = 24

So the average speed is 24 mph. If this seems strange to you, consider that more time is spent traveling at 20 mph than time spent at 30 mph, so the "20 mph" figure should count more toward the average.