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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?
There are two numbers whose sum equals the difference of their squares.
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?
A four-sided town measures 1100 feet on one side and 1000 feet on the other side, on one edge 600 and the other edge 600.
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?
A merchant bought 50,000 pounds of pepper in Portugal for 10,000 scudi and paid a tax of 500 scudi.
Find a number having remainder 29 when divided by 30 and remainder 3 when divided by 4.
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.
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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