Coffee to Go
132 Fast Food Lane
Partially Hydrogenated, WI 33021
November 3, 1997
Math 101 Students
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
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.