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.). 1 yard (yd.). Surveyors' Measure 25 links 1 rod. 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 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. 16 ounces (oz.) 1 pound (lb.). 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.). APOTHECARIES' WEIGHT 1 pound (lb.). |