Diff EQ in Camelot In the Kingdom of Camelot, a member of the royal council has

Question

Diff EQ in Camelot

In the Kingdom of Camelot, a member of the royal council has been murdered. The body is discovered at noon, and the court physician measures the temperature of the body at 30 degrees Celsius. The following individuals are identified as suspects:

1)      Arthur, prince and future king of Camelot, who has an alibi from 8:15 to 9:15 and then from 9:45 to 10:45 that morning

2)      Guinevere, servant to the king’s ward, who has an alibi from 7:15 to 8:30, 9:00 to 9:30, and 10:00 to 11:00 that morning

3)      Gawain, his workout partner, who has an alibi from 7:00 to 8:00, 8:30 to 10:00, and 10:30 to 11:00 that morning

4)      Merlin, court magician, has an alibi from 7:45 to 8:45 and then from 9:30 to 10:45 that morning

One hour later, the physician measures the body temperature at 27 degrees. Assume that the surrounding air temperature at the murder site has remained constant at 19 degrees, and that a human’s normal body temperature is 37 degrees. You do not have to solve the entire problem, but you must assist us in determining who is responsible for the murder.

Explanation / Answer

Correct answer is:

2)      Guinevere, servant to the king’s ward, who has an alibi from 7:15 to 8:30, 9:00 to 9:30, and 10:00 to 11:00 that morning

Explanation:

The temprature of body is 30 degree celcius at noon and 27 degree celcius one hour later. It means, temperature of body is falling at the rate of 3 degree celcius per hour or 1 degree celcius every 20 minutes (estimated).

Since temperature of human's normal body is 37 degree celcius and it was measured to be 30 degree celcius at noon, it means murder took place around 2 hours and 20 minutes prior to noon. Which means, estimated time of murder is 9.40 AM.

Option 3) and option 4) are wrong because both were absent at 9.40 AM. Means, either option 1) is true or option 2) is true.

Prince is present during 9.15- 9.45 AM whereas Servant is present during 9.30-10 AM. During 9.30-9.45 AM, both are present so no one killed. It means, when prince left at 9.45, servant murdered and left at 10 AM.

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