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A Diet of Problems From An Unknown Source

While cleaning out someone's file cabinet, I found a 13-page document containing miscellaneous mathematics problems...appropriate for secondary students. Some of the more unusual problems are these...Try to solve them....Share them...

  1. The average flight velocity of an African Swallow is 17/3 that of the European Swallow. An African Swallow and two European Swallows collaborate in transporting 50 coconuts a distance of 6 KM. If the average velocity of an European Swallow is 9 KM/hour while carrying a coconut and 18 KM/hour while unburdened, how many minutes will the job require? (i.e. when will the Swallow carrying the last coconut pass the 6 KM mark?)
  2. What is the value of the real root of the polynomial equation x3 + (3+14i)x2 + (51+42i)x + 153 = 0.
  3. Janice is hiking along some trails near Yelm. From her compass readings she knows she is 9 miles west and 12 miles south of Haugland's Concrete. She also knows she is 8 miles east and 3 miles north of Diana's Bear Den. Highway 161 runs straight between these two places. It is starting to rain; Jancie wants to reach the highway as soon as possible. To the nearest tenth of a mile, what is the shortest distance she will have traveled to reach the highway?
  4. The probability that Gertrude's dog Fido will bite Bob, the milkman, varies depending on the temperature (in Farenheit) according to the following equation: P(A)*T = 18. However, as the temperature gets colder, Bob wears thicker clothing, so the probability of Fido's teeth finding his skin follows this relation: P(B) = T/100. At 32 degrees, what is the probability that frisky Fido will make Bob bleed?
  5. A 30-sided die numbered from 1 to 30 has half triangular and half square faces. On a given roll, a square face is twice as likely to end up on the bottom as a triangular face. Only odd numbers appear on the triangular face, and only even numbers are on the square faces. What is the probability that the sum of two consecutive rolls of the die will be even? (Note: The value of a roll is read off the bottom of the die.)
  6. How many factors will the product of 2 prime numbers have? (My Additional question: How many factors will the product of n prime numbers have?
Be aware that you may need to make some reasonable assumptions in order to both understand and solve these problems. But, that is part of the fun in mathematical problem solving!


Hint: No hints provided.


Solution Commentary: No solutions provided...unless someone send them in with reasoning....Hint...Hint...