Frank Morgan's Math Chat
May 6, 1999
OLD CHALLENGE. A physicist and a mathematician can clean a house in 6 hours; an engineer and the mathematician in 3 hours; and the physicist and the engineer in 1 hour and 12 minutes. How long would it take the physicist alone?
ANSWER (Derek Smith). Three hours. In six hours, P and M can clean 1 house, E and M can clean 2 houses, P and E can clean 5 houses, so 2P = (P + M) - (E + M) + (P + E) can clean 1-2+5 = 4 houses. Hence one physicist can clean 2 houses in six hours, or 1 house in three hours.
This is faster than the physicist and mathematician working together! The mathematician must be slowing things down. Readers supply a number of different interpretations:
"With horror, we note that, as given, the mathematician's rate is actually negative; he/she must be making a mess rather than cleaning. A calumny!" -Elliot Kearsley
"El matemático es una carga." Juan José López Ordóñez, University of Granada, Spain ["Carga" is a wonderful Spanish word meaning "burden" or "millstone around their necks."]
"I have known some mathematicians like that." -Joe Shipman
"Since my wife has been telling me for many years that I actually hinder rather than help cleaning the house, I believe that my solution is correct." -Michael Marcotty
"So, why is the room most in need of cleaning in our school the Physics lab?" -Richard Ritter
I think that the best explanation comes from Al Zimmermann:
"Clearly the mathematician's conversation is so incredibly engaging as to distract any coworkers from the task at hand."
NEW CHALLENGE (John Snygg). A mathematician, lost in the desert, hears a single toot from a train due west. He knows that the train goes at constant speed in a straight line, but he forgets in which direction. What direction should he walk?
Send answers, comments, and new questions by email to Frank.Morgan@williams.edu, to be eligible for Flatland and other book awards. Winning answers will appear in the next Math Chat. Math Chat appears on the first and third Thursdays of each month. Prof. Morgan's homepage is at www.williams.edu/Mathematics/fmorgan.
Copyright 1999, Frank Morgan.