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Problems from Another Time

Individual problems from throughout mathematics history, as well as articles that include problem sets for students.

Two bicyclists travel in opposite directions around a quarter-mile track and meet every 22 seconds. When they travel in the same direction on this track, the faster passes the slower once every 3 minutes and 40 seconds. Find the rate of each rider
The purchase price for an apple and an orange is 100 yen. When n oranges and n + 3 apples are bought the price is 520 yen. Find the number n of oranges and the price of one orange.
A circle is inscribed in an isosceles trapezoid. Find the relationship of the radius to the sides.
Having been given the perimeter and perpendicular of a right angled triangle, it is required to find the triangle.
A carpenter has undertaken to build a house in 20 days. He takes on another man and says; "If we build the house together, we can accomplish the work in 8 days!" How long would it take this other man to build the house working alone?
Determine the dimensions of the least isosceles triangle ACD that can circumscribe a given circle.
A fellow said that when he counted his nuts by twos, threes, fours, fives and sixes, there was still one left over; but when he counted them by sevens they came out even. How many did he have?
Given four numbers whose sum is 9900; the second exceeds the first by 1/7 of the first...
A general formed his men into a square, that is, an equal number in rank and file, and he found that he had an excess of 59 men.
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.

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