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Problems from Another Time

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

Given a guest on horseback rides 300 li in a day. The guest leaves his clothes behind. The host discovers them after 1/3 day, and he starts out with the clothes.
A bridge is built across a river in 6 months by 45 men. It is washed away by the current. Required the number of workmen sufficient to build another of twice as much worth in 4 months.
The perimeters of two similar triangles are 45 and 135 respectively. One side of the first triangle has length 11″ and a second side, 19″. Find the lengths of the sides of the second triangle.
The triangle ABC has a right angle at C. Show that 1/ED=1/AC+1/AB