Monday, October 19, 2009

Averaging the Speed

You decide to take your kids to a new fascinating movie experience: "Cloudy with a chance of meatballs" in 3D. Rushing to get to the theater in time you speed at 50mph on a 35mph road. On the way back you are trying to demonstrate to your kids that you are driving according to the law "on average" and therefore you go very slowly, at 25mph. Will your average speed be lawful?

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Kim said...

I would average 33.33 MPH, just under the legal limit of 35mph -- but, I think we can all agree, that doesn't change the fact that I would have been over the limit half the time and setting a bad example for the kids.

Kim said...

(Actually, I would have been over the limit half the distance, but only one-third of the time)

Maria said...

Kim, you did it again!

This is a great puzzle to share with your kids, after taking them to this amazing 3D movie (with a lawful speed). From the first glance it seems that the average speed should be:
(50mph + 25mph)/2 = 37.2mph

But thinking deeper, we realize that we drove the same distance with 50mph and back with 25mph, so we must have spent twice as much time on our way back than on our way to the theater. So, we drove time T with 50mph and 2xT with 25mph. The average will be not in the middle of 25 and 50, but twice closer to 25mph:
(T x 50 + 2 x T x 25) / (3 x T) = 100 / 3 = 33.3mph as Kim correctly proclaimed.

New puzzle tomorrow.

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