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Coffee to Go

J.I.T. Box
132 Fast Food Lane
Partially Hydrogenated, WI 33021
November 3, 1997

Math 101 Students
Wheaton College
Norton, MA 02766

Dear Calculus Students:

After the recent McDonald's verdict, my company, which owns a series of quick-dining establishments has been hit with a series of copy-cat lawsuits. We need some technical expertise on one of these matters, and your enterprising and resourceful professor referred me to you.

The plaintiff, whom I will refer to as R. Clumsy for legal reasons, was the passenger in an automobile that stopped at one of our drive-through windows early one morning for coffee. Mr. Clumsy placed the coffee in a cup holder for several minutes; held the coffee cup in his hands for a short time; and then he spilled the coffee. He maintains that the coffee was much too hot, and he is suing for $200,000 for emotional distress and dry cleaning bills.

I would like to know how credible his story is. While we do serve our coffee at 160 degrees F, I do not believe that the coffee was above the industry standard of 140 degrees F when Mr. Clumsy spilled his coffee. He claims that it was exactly 7:58 am when the coffee was poured, and when he spilled the coffee, some of it fell on his watch, a cheap Timex ripoff, which stopped at precisely 8:08 am. He says that he left the coffee in the cup holder for 5 minutes, and held it in his hands for another 5 minutes before spilling it. I would like to be able to raise a reasonable doubt about the credibility of his story, either by showing that the temperature was not above the industry standard, or by showing that if the times are slightly different than he claims, then the coffee was not too hot.

Assuming Mr. Clumsy's scenario is correct, I would like to know if the temperature of the coffee was above the industry standard when he spilled it. I am doubtful that he remembered the times exactly. In particular, I seriously doubt that the coffee was in the cupholder and in his hands for exactly five minutes. What would the temperature be if the breakdown were 4 minutes in the cupholder and 6 minutes in his hands? 6 minutes in the cupholder and 4 minutes in his hands? 7 minutes in the cupholder and 3 minutes in his hands? I am also a little dubious about his claim that the coffee was poured at 7:58 am exactly. What would the result be if the coffee were poured at 7:56 am instead? In your report, I would like your expert opinion on whether or not there exists a reasonable doubt that the coffee was above 140 degrees.

To help you out, the top investigators in our Fact Finding Department have uncovered the following information. Mr. Clumsy lives 7.8 miles away from the restaurant, so you can assume that the passenger compartment of the car had warmed to a comfortable 72 degrees, which is the same temperature that we keep the restaurant. Further, if you take a fresh, delicious, aromatic cup of our coffee and place it in a room at 72 degrees, then it will cool to 149 degrees in four minutes and thirty seconds. We also asked Mr. Clumsy to hold a thermometer in his hands just like he held the coffee. We discovered that the temperature was 92.3 degrees.

I understand that this is a busy time of the semester for you, but I would greatly appreciate your report by November 14, since the trial is set to begin the next week.

Yours sincerely,
J.I.T. Box

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