This is an interesting problem from 180 BC China.

“In one day, a person can make 30 arrows or fletch [put the feathers on] 20 arrows.  How many arrows can this person both make and fletch in a day?”

It turns out the solution to this problem led me into the history of numerator/denominator (aka common) fractions, a subject I had been finding difficult to track down.

Answer.

See Making Arrows for a solution.