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

21
4. If 5 oxen or 7 horses eat up the grass of an enclosure in 74
days; in what time could 5 horses aiid 7 oxen eat up the grass of the
enclosure?
5. If ~17. 10s. be gained by a principal of ~75 in 9 months; at
-what rate is that per cent. per annum?
6. If a tradesman with a capital of ~2000 gain ~50 in 3 months;
what sum will he gain with a capital of ~3000 in 7 months?
7. If 15 horses and 148 sheep can be kept 9 days for ~75. 15s.;,what sum will keep 10 horses and 132 sheep for 8 days, supposing,5 horses to eat as much as 84 sheep?
8. If 5 men can reap a field whose length is 800 feet and breadth
700 feet in 3 cl days of 14 hours each; in how many days of 12 hours
each can 7 men reap a field 1800 feet long and 960 broad?
9. If 25 labourers can dig a ditch 220 yards long, 3ft. 4in. wide,:and 2ft. 6in. deep, in 32 days, when the day is 9 hours long1; how
many labourers would be able to dig a ditch half a mile long, 2ft.
4in. deep, and 3ft. 6in. wide, in 36 days, when the day is 8 hours
long?
XXI.
1. If a person travels over 120 miles in 9 days, when the days
-are 8 hours long; in how many days of 16 hours each will he travel
over 640 miles?
2. A is 20 miles behind B, A travels at the rate of 51 miles an
hour, and B at the rate of 3- miles an hour; after what time will
A overtake B?
3. If 54'32 Irish miles are equivalent to 69*14 English; how
many English correspond to 15L- Irish?
4. What fraction of an inch on a globe of 50 inches diameter
"would represent the altitude of Chimborazo, 21,424 feet high, the.highest point of the Andes, supposing the earth a sphere, and its
diameter 8000 miles?
5. If the shadow of a tower be 80ft. 6in., and that of a stick 3ft.
long placed perpendicularly at the same minute be 5ft. 2in.; find the
height of the tower, and state the Prop. in Euclid which you employ.
6. The ratio between the polar and equatorial diameters of the
earth is 283-33 to 299-33, and the length of the polar diameter is
7899*114 miles; find the length of the equatorial diameter.
7. Assuming that the circumference of a circle is to its diameter
as 22 to 7, and that the circumference of the earth is to its diameter
as 160 metres to 167 feet, determine to five places of decimals the
ratio of a metre to a foot.
8. How much larger does the full earth appear to the inhabitants
of the moon (if there be any) than the full moon to the inhabitants of
the earth, supposing the diameters of the earth andl moon are 8000
and 2000 miles respectively, and that the areas of circles are propor-tional to the squares of their diameters.?