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Can you explain why Marilyn vos Savant was wrong?

Asked by LostInParadise (18208 points ) June 26th, 2014

Marilyn vos Savant writes the Ask Marilyn column in the Parade Magazine newspaper supplement. In her last column, she inadvertently created a nice little math problem. She did this by incorrectly answering a fairly non-interesting math problem. What is of interest is showing why an assumption she made was incorrect.

You can read the original problem here

This is my conversion of her original. Two people, a and b working together can complete a project in 6 hours. We know that if each of them works at the same rate as the other (assuming no synergy), it would take each of them 12 hours to complete the project on their own. In this case the sum of their work times is 24.

Suppose that a works faster than b. Marilyn assumed that the sum of their work times is still 24. Come up with an argument to show that the sum of their work times must in fact be greater than 24. You can in principle explain this with no algebra, but you might want to use algebraic notation to simplify the explanation.

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