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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 man is walking across a bridge, when a boat passes under the bridge.How rapidly are the boat and the pedestrian separating after the boat passes under the bridge?
How long does it take a single man to do work when...
Two officers each have a company of men, the one has 40 less than the other.
There are two numbers whose sum equals the difference of their squares.
Given the dimensions of an isosceles trapezoid find the length of the transversal drawn parallel to the bases that divides the trapezoid into 2 equal areas.
A leech invited a slug for a lunch a leuca away.
The number 50 is divided by a certain number. If the divisor is increased by 3, the quotient decreases by 3.75. What is the number?
Given a pendulum as shown. The height of the pendulum is two units and its horizontal width is 2 units. What is the area of the pendulum?
My age is a number consisting of two digits, 1/2 of this number is a mean proportional between these two digits, and two years hence, my age will be a third proportional to the same two digits, directly as they stand in my present age.
Find a number having remainder 29 when divided by 30 and remainder 3 when divided by 4.