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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 men rent a pasture for 100 liras on the understanding that two cows are to be counted as being equivalent to three sheep. The first puts in 60 cows and 85 sheep; the second 80 cows and 100 sheep. How much should each pay?
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
Having been given the perimeter and perpendicular of a right angled triangle, it is required to find the triangle.
On a certain ground stands two poles 12 feet apart, the lesser pole is 35 ft. in height and the greater 40 ft. It is sought, if the greater pole will lean on the lesser, then in what part will it touch?
The edge of a cloud is at an altitude of 20 degrees and the sun above it at 35 degrees. The shadow cast by the edge of the cloud fall on a object 2300 yards away, how high is the cloud?

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