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7. The time to go 1 mi. up stream = 4 hr. 8. The time to go 1 mi. down stream = t hr. 9. The time to go 1 mi. up and return 1 hr. + 1 hr. = $hr 10. Since in } hr. the boat can go and return 1 mi., 11. In 1 12.

36 mi. .. in 12 hr. the boat can go 36 mi, and return.

3 mi.,

12 16

29. The rate of the current of a river is 4 miles an hour. How far down the river can a boat go and return in 18 hours, if the boat's rate of travel in still water is 6 miles an hour?

30. In a river in which the rate of the current is 1.5 miles an hour, a boat travels 18 miles down stream in 3 hours. In what time can the boat return ?

31. In a pasture where the grass is growing at a uniform rate, 13 cows can eat off the grass in 5 weeks, and 9 cows can eat off the grass in 9 weeks. How long will it take 7 Cows to eat it?

32. A wolf is 84 leaps in advance of a dog. The wolf takes 8 leaps to the dog's 6, but 2 of the dog's leaps equal 5 of the wolf's. How many leaps must the dog take to catch the wolf?

SOLUTION: 1. The dog takes 6 leaps to the wolf's 8 leaps. 2.

1 leap 3. But 2 of the dog's leaps = 5 wolf-leaps. 4. .. 1 " 5. wolf-leaps - wolf-leaps = 1 wolf-leaps. 6. For the dog to gain } wolf-leaps, he must take 1 leap. 7. 1 wolf-leap,

옥 8. 84 wolf-leaps,

72 leaps. .: the dog can catch the wolf in 72 leaps.

=

33. A fox is 60 leaps ahead of a hound, and takes 4 leaps while the hound takes 3; but 1 of the hound's equals 2 of the fox's leaps. How many leaps must the hound take to catch the fox?–Milne, p. 349.

34. A boat goes 18 miles an hour down stream, and 12 miles an hour up stream: if it is 20 hours longer in coming up than in going down, how far down did it go?

35. A boy is flying a kite with a string 225 feet long. If it is 112 feet from where the boy stands to a point directly under the kite, how high is the kite, allowing 13 feet for the sag of the string?

CHAPTER IX

DENOMINATE NUMBERS

210. A denominate number (Latin denominare, to name) is a number in which the unit or units are named.

211. A simple denominate number is one composed of but one denomination; as, 5 tons.

212. A compound denominate number is one composed of two or more denominations; as, 6 bu. 3 pk.; 5 yd. 2 ft.

213. Reduction is the process of changing a number from one denomination to another without changing its value. Reduction is of two kinds—ascending and descending.

214. Reduction ascending is the process of changing a number from one denomination to a higher denomination. Thus, 16 pk. 4 bu.

215. Reduction descending is the process of changing a number from one denomination to a lower denomination. Thus, 4 bu. = 16 pk.

TABLES

216. The tables given here are those which the ordinary citizen is most likely to need. If one is to enter a business in which special measures are used, the tables should be learned then as a part of his preparation for that business.

I. MEASURES OF EXTENSION

LINEAR MEASURE

Common Measure

12 inches (in.) = 1 foot (ft.).
3 feet

1 yard (yd.).
5} yards, or 164 feet = 1 rod (rd.):
320 rods, or 5280 feet = 1 mile (mi.).

Surveyors' Measure
7.92 inches = 1 link (li.).

25 links 1 rod.
100 links = 1 chain (ch.).
80 chains 1 mile.

SQUARE MEASURE

144 square inches (sq. in.) 1 square foot (sq. ft.). 9 square feet

= 1 square yard (sq. yd.). 304 square yards = 1 square rod (sq. rd.). 160 square rods

1 acre (A.).
= 1 square mile (sq. mi.).

1 section. 36 sections

= 1 township. NOTE.-In measuring roofs, etc., 100 sq. ft. = 1 square.

640 acres

1 mile square

CUBIC MEASURE

1728 cubic inches (cu. in.) 1 cubic foot (cu. ft.). 27 cubic feet

1 cubic yard (cu. yd.). 128 cubic feet

= 1 cord.

[blocks in formation]

16 ounces (oz.) 1 pound (lb.).
100 pounds 1 hundredweight (cwt.).

20 hundredweight = 1 ton (T.). NOTE.—This table is used in weighing almost everything in common use, except gold and silver.

TROY WEIGHT

24 grains (gr.) 1 pennyweight (pwt.).
20 pennyweights 1 ounce.
12 ounces = 1 pound.
NOTE.-Troy weight is used for precious metals.

APOTHECARIES' WEIGHT
20 grains (gr.) 1 scruple (sc., or ).
3 scruples 1 dram (dr., or 3).
8 drams 1 ounce (oz., or 3).
12 ounces

1 pound (lb.).
NOTE.—This table is used in selling drugs at retail.

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