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Problems from Another Time

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

A cylindrical tin tomato can is to be made which shall have a given capacity. Find what should be the ratio of the height to the radius of the base that the smallest possible amount of tin shall be required.
There is a four-sided field whose eastern side measures 35 paces, its western side 45 paces, its southern side 25 paces and its northern side 15 paces. Find the area of this field.
A round pond sits in a rectangular garden. Its center is inaccessible; however, you know the distances from each corner of the garden to the center of the pond: 60, 52, 28, and 40 yards. What is the radius of the pond?
A circle is inscribed in an isosceles trapezoid. Find the relationship of the radius to the sides.
The sum of the two digits of a 2-digit number is 9. If 45 is subtracted from the number, the result will be expressed by the digits in reverse order. Find the number.
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?
To find three quantities x.y, and z...
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?
There are two numbers which are to each other as 5 and 6 and the sum of their squares is 2196. What are the numbers?
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?

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