Problems from Another Time

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

The cost per hour of running a certain steamboat is proportional to the cube of its velocity in still water. At what speed should it be run to make a trip up stream against a four-mile current most economically?
An official asks a woman why she has so many bowls to wash. The woman explains that she had dinner guests who ate meat, rice, and soup. Judging by the number of bowls, how many guests were there?
Divide 100 loaves of bread among 10 men including a boatman, a foreman, and a doorkeeper, who receives double portions. What is the share of each?
A set of n disjoint, congruent circles packs the surface of a sphere S so that each region of the surface exterior to the circles is bounded by arcs of three of the circles.
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
An oracle ordered a prince to build a sacred building, whose space would be 400 cubits, the length being 6 cubits more than the width, and the width 3 cubits more than the height. Find the dimensions of the building.
Having been given the perimeter and perpendicular of a right angled triangle, it is required to find the triangle.
Now a good horse and an inferior horse set out from Chang'an to Qi. Qi is 3000 li from Chang'an.
A water tub holds 73 gallons; the pipe which fills it usually admits 7 gallons in 5 minutes; and the tap discharges 20 gallons in 17 minutes.
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?