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Problems from Another Time

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

What is the sum of the reciprocals of the triangular numbers?
Now a good horse and an inferior horse set out from Chang'an to Qi. Qi is 3000 li from Chang'an.
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?
Suppose the area of an equilateral triangle be 600. The sides are required.
Find two number with sum 20 and when squared their sum is 208.
A lady has two silver cups, and only one cover for both. The first cup weighs 16 oz, and when it is covered it weighs 3 times as much as the second cup; but when the second cup is covered, it weighs 4 times as much as the first.
Make of 10 three parts such that one part multiplied by 3 makes as much as the other multiplied by 4 and as the other multiplied by 5.
Given the cats eye as shown. Let the radius of the eye be given by R. What is the area of the pupil?
Three hundred pigs are to be prepared for a feast.
X, Y and Z hired a pasture for the season for $90.00. Each has a different number of mules and are on the pasture for a different number of days. How much is each to pay?