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7. The time to go 1 mi. up stream = hr.

8. The time to go 1 mi. down stream = hr.

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hr.hr. = hr

9. The time to go 1 mi. up and return 10. Since in hr. the boat can go and return 1 mi.,

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

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.

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5. wolf-leaps-wolf-leaps = wolf-leaps.

6. For the dog to gain wolf-leaps, he must take 1 leap.

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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.

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

CUBIC MEASURE

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1728 cubic inches (cu. in.) = 1 cubic foot (cu. ft.).

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20 hundredweight = 1 ton (T.).

NOTE. This table is used in weighing almost everything in common use, except gold and silver.

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NOTE.-Troy weight is used for precious metals.

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NOTE. This table is used in selling drugs at retail.

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