College Algebra & Trigonometry, 2018a

1.9. RATIONAL EQUATIONS 83
19) A living room shelf is 36 inches long and contains a certain number of
books of uniform width. If each book were one-half inch narrower, the shelf
would hold six more books. How many books of the wider variety does it hold?
20) I am a brazen lion; my spouts are my two eyes, my mouth and flat of my
right foot. My right eye fills a jar in two days, my left eye in three and my foot
in four. My mouth is capable of filling it in six hours. Tell me how long all four
together will take to fill it. (Ancient Greece)
21) A man wishes to have 500 rubii of grain ground. He goes to a mill that has
five stones. The first stone grinds 7 rubii of grain in an hour, the second grinds
5 rubii in an hour, the third 4 rubii in an hour, the fourth grinds 3 rubii per hour
and the fifth grinds 1 rubii per hour. In how long will the grain be ground and
how much is done by each stone? (Clavius, German 1583)
22) If two men and three boys can plow an acre in one-sixth of a day, how long
would it require three men and two boys to plow it?
(Edward Brooks, American 1873)
23) A cobbler can cut leather for ten pairs of shoes in one day. He can finish 5
pairs of shoes in one day. How many pairs of shoes can he both cut and finish in
one day? (Ancient Egypt)
24) Four waterspouts are filling a tank. Of the four spouts, one can fill the tank
in one day, the second takes two days, the third takes three days and the fourth
takes four days. How long will it take all four spouts working together to fill the
tank? (Ancient Greece)
25) If, in one day, a person can make 30 arrows or fletch [put feathers on] 20
arrows, how many arrows can this person both make and fletch in one day? (Ancient
China)