Elementary arithmetic, with brief notices of its history... by Robert Potts.

28
in 1 hour, and C finishes it in 20 minutes. How long would they
have been in doing the whole if they had worked together?
8. If A can perform a work in 9 days, B in 10, and C in 11, in
what times could A and B, A and C, and B and C respectively complete the work?
9. A, B, and C can each complete a certain work in 9, 12, and 18
days respectively. If A and B work together for 2 days, and A and
C afterwards for 2 more, how long will B and C working together take
to finish the work?
10. If A can do as much work in 5 hours as B can do in 6 hours, or
as C can do in 9 hours, how long will it take A to complete a piece of
work, one half of which has been done by B working 12 hours, and C
working 24 hours?
11. If A in 2 days can do as much work as C in 3 days, and B in 5
days as much as C in 4 days, how long will B require to execute a piece
of work which A can accomplish in 6 weeks?
12. A is twice, and B is just one and a half times as good a workman as C. The three work together for two days, and then A works
on alone for half a day, and B for one day. How long would it havo
taken A and C together to complete as much as the three will have
thus performed?
13. If A can by himself perform a certain quantity of work in 5
days, B twice as much in 7, and C 4 times as much in 11 days,
in what time can A, B, and C together perform 3 times the original
quantity?
14. A can do as much work in 2 days as B in 3 days, and B
as much in 4 days as C in 5 days. In what time could A, B,
and C together do a piece of work which A can do in 11 days?
XXXI.
1. If a cubic foot of water weigh 1,000 ounces avoirdupois, find the
number of grains Troy in a cubic inch of water.
2. A rectangular tank is 13 feet 6 inches long by 9 feet 9 inches
wide. How many cubic yards of water must be drawn off to make the
surface sink 1 foot?
3. How many tons of water will a cistern contain whose length,
breadth, and depth are respectively 18 feet 8 inches, 10 feet 4 inches,
and 6 feet 9 inches? What is the amount of pressure of the wator on
the bottom of the cistern?
4. If 13 cubic feet make 81 gallons, how many hogsheads will
be contained in a cistern 42 feet long, 39 feet broad, and 10- feet
deep?
5. A cistern is 2- full of water, and after 35 gallons are drawn
off it is found to be - full. How many gallons does it contain?
6. Two equal wine-glasses are filled with a mixture of spirit and
water, one containing 3 parts of water and one part of spirit, and the