Tuesday, September 24, 2013

Paradox?

No, this isn't really a paradox, it's just an unexpected, counter-intuitive  result. So... you travel from A to B (doesn't matter how far it is) at 40 mph and then travel back from B to A at 60 mph.  What is your average speed - 50 mph, yes?  Well, do the maths.  Speed is distance divided by time, so time is distance divided by speed, right?  So time to get there is d (whatever it is) /40 and time to come back is d/60. So total time for the trip (2d) is d/40 + d/60, which is 10d/240 or 5d/120.  Going back to our original statement that speed is distance divided by time, then the speed for the round trip is 2d divided by 5d/120.  We can ignore the "d"s which cancel each other out so the calculation becomes 2 divided by 5/120, which as I'm sure you remember from school is the same as 2 multiplied by 120/5, which is 240/5 which comes out as 48.  So your average speed is in fact 48mph.  No what you expected was it?

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