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Problems from Another Time

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

If 12 cattle eat up 3 1/3 acres of meadow in 4 weeks and 21 cattle eat up 10 acres of exactly similar meadow in 9 weeks, how many cattle shall eat up 36 acres in 18 weeks? (Hint: The grass continues to grow.)
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.
Suppose a lighthouse is built on the top of a rock; the distance between a place of observation and that part of the rock level with the eye is 620 yds.
In a forest, a number of apes equal in number to the square of 1/8 of the total number of apes are noisy. The remaining 12 apes are on a nearby hill irritated. What is the total number of apes in the pack?
Determine the dimensions of the least isosceles triangle ACD that can circumscribe a given circle.
Given four numbers whose sum is 9900; the second exceeds the first by 1/7 of the first...
Find the area of the elliptical segment cut off parallel to the shorter axis;
A number of 3 digits in base 7 has the same three digits...
If two Post-boys, A and B at 59 miles distance from one another, set out in the morning in order to meet...