Saturday, May 26, 2007

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.

1 comment:

mike 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.