Drive to the Store

You drive to the store at 20 mph and return by the same route at 30 mph. Discounting the time spent at the store, what was your average speed?

Answer

The average speed is 24 mph, not 25mph.

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 that is strange, assume that the distance to the store is 60 miles. When you drive at 20 mph, you will take 3 hours. When you drive at 30 mph, you will take 2 hours. The total time taken is 5 hours and the total distance travelled is 120 miles. So the average speed is: 120 / 5 = 24 mph.

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