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Problems from Another Time

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

The steamer, Katie, leaves the wharf at New Orleans and runs an average speed of 15 mph. When Katie had gone 25 miles, the steamer R.E. Lee leaves the wharf and runs the average speed of 18 mph. How far will the Lee go before she overtakes the Katie?
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
Find two numbers such that multiplying one by the other makes 8 and the sum of their squares is 27.
A farmer sold a team of horses for $440, but did not receive his pay for them until 1 yr, 8 mo after the sale. He had at the same time another offer of $410 for them. Did he gain or lose by the sale and by how much, money being worth 6%/yr?
There is a lion in a well whose depth is 50 palms. He climbs and slips back a certain amount each day. In how many days will he get out of the well?
Find two numbers, x and y, such that their sum is 10 and x/y + y/x = 25
What is the sum of the reciprocals of the triangular numbers?
A father wills his estate valued at $40, 000 to his three children. Before the settlement one of the children dies. What should the other two receive?
Of the two water reeds, the one grows 3 feet and the other 1 foot on the first day. The growth of the first becomes every day half of that of the preceding day, while the other grows twice as much as on the day before.
Suppose the area of an equilateral triangle be 600. The sides are required.

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