Math Question

5 miles per hour is equivalent to 1 hour per 5 miles, right? So how come you can't say 1/5 h/m +1/5 h/m = 5 m/h +5 m/h? Is there some kind of reciprocal for addition?
I think maybe we treat adding sppeds as fractional addition, but it's actually something else that just happens to look like addition of fractions, but isn't, really.


Mike Stay said…
If (in outer space so gravity's irrelevant) you're traveling 5mph and throw a ball at 5pmh, the total speed (ignoring relativity and assuming you're much more massive than the ball) will be 10mph--that is, twice five miles over the same hour.

If you throw a ball at 1/5 hpm, wait for it to traverse 5 miles, then throw another, the two balls together travel at 2/5 hpm--that is, it takes two hours for the balls to traverse the same 5 miles.

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