48. If 1447b. avoirdupois be equal to 175lb. troy, how much troy weight is equal to 120lb. avoirdupois ? 49. If 60 gallons of water, in one hour's time, fall into a cistern containing 200 gallons; and by a pipe in the same cistern there runs out 45 gallons in an hour: in how many hours will it be filled? 2.01 50. If a shadow 6 feet in length is cast by a pole 14 feet high, how high is that steeple which at the same time casts a shadow 90 feet long? 51. If 74 men had provision for 35 days; but after 5 days, 20 men were sent away: how long will the provision last the remaining 54? 52. If a man complete a journey of 25 days at 9 hours' walking each day: how long would he have been, if he had travelled 13 hours a day? 53. If a stick 3 feet high project a shadow 2 feet 8 inches, what must be the height of a tower whose shadow measures 74 feet? 54. At 71⁄2cts. per lb. what will 10cwt. 2qr. 16lb. of rice come to? 55. Suppose 50 men to finish a piece of work in 48 days, how many are sufficient to finish it in 32 days? 56. If 18 men can perform a piece of work in 28 days, how many men can do it in one-fourth part of the time? 57. Suppose 60 men to complete a piece of work in 71 months, how many could finish it in 9 months? 58. My year's rent of 350 acres of land is $500, and sundry taxes $27.50: what does my farm bring me per acre? 59. If $200 in 12 months gain $10 interest, what will $750 gain in the same time? 60. How many yards of stuff, 3 quarters wide, are equal in measure to 36 yards of 7 quarters wide? 61. What must be the width of a court yard which is 50 feet long, to be equal in measure to another that is 125 feet long by 20 feet broad? 62. If 12 inches long require 12 inches broad to make a square foot, what length will 8 inches broad require ? 63. How many yards of paper, 27 inches wide, will hang a room that measures 60 feet round and 9 feet high? 64. If 220 yards in length, and 22 in breadth, make an acre, what must be the length when the breadth is 36 yards? 65. If the carriage of 37 cwt. for 56 miles come to $26, how far can I have 259 cwt. carried for the same sum? 66. If 5000 yards of cloth, 5 quarters wide, will make coats for 2000 men, how many yards of shalloon, of 3 quarters wide, will line them? 67. If 49cwt. 2qrs. are carried 150 miles for a certain sum, what distance would 198cwt. be carried for the same? 68. If 144 cwt. be carried 200 miles for $32, how many pounds can I have carried 72 miles for the same money? 69. If ounces cost £, what will 1 ounce cost? 70. If of a sloop cost $420, what is 1/3 of her worth? 71. If of a gal. of wine cost $5 what will of a tun cost? 72. A merchant bought 3 pieces of silk, each containing 24 yards, at 45 cents per yard: what does the whole come to ? 73. A person having of a coal mine, sells of his share for $342: what is the whole mine worth? 74. If of a ship be worth $560, what part of her may be purchased for $1920? 75. If 3 times 3 pound cost 1 times 1 dollars, what is the value of of of of 392 pounds? 76. If 3 yards of cloth, that is 13 yards, wide, be sufficient to make a cloak, how much Persian, which is but yards wide, will be required to line it? 77. In exchanging 20 yards of cloth, of 11 yards wide, for some of the same kind of yards wide, what quantity of the latter makes an equal barter? 78. If the penny loaf weigh 14 ounces, when wheat was 4 shillings per bushel, what must it weigh when wheat is at 7 shillings per bushel ? 79. Bought 5.8 tuns of oil for $338.64, whereof 50.6 gallons leaked out; how much must the remainder be sold for per gallon, that the purchaser may be no loser? 80. A lends B 100 dollars for 6 months; what sum should B lend A for 35 years to requite his kindness? 81. If 1.47cwt. of sugar cost $6.86, what are 1.2lbs. worth? 82. What are 7.8yds. worth, if .5 of a yard cost $4.50? 83. What is the value of 443.875 barrels of flour, if 5.75. barrels cost $30 ? 84. If 21 men have built a wall in 1.75 days, how many men must be employed to build it in .25 of a day? 85. There are two numbers to one another as 16 to 17, the lesser is 65.525, what is the greater? 86. If a pasture serve 36 cows for 75 days, how many cows would eat it in 25 days? N 87. Of a piece of cloth, containing 20.125 yards, a part was sold for $5.46; what quantity remained, supposing the whole to be worth $18.35? 88. If a ball of 1876. be shot from a cannon with such a force as to cause it to move 100ft. in a second, how fast would a 2476. ball move, driven by the same force? 89. If a ship sail 180 miles in 15 hours, how many hours will it require to sail 60 miles? 90. If 12.8yds. cost $10.125, what cost 5.36 E. English? 91. If the earth performs its diurnal revolution in 24 hours, in what time does it move through 1 degree? 92. If a common field will feed 520 sheep 90 days, how long will it feed 600 sheep? 93. Suppose a haymow to be sufficient for 40 head of cattle 18 weeks, how long would it serve 60 head of cattle? 94. If 1000 men, in a garrison, have provision for 6 months, how long would the same provision last 1500 men? 95. If a certain number of men can throw up an entrenchment in 9 days, when the days are 16 hours long, what time will it take when the days are 12 hours? 96. If a person can perform a journey in 6 days, riding 9 hours each day, how long will it take him if he rides 12 hours a day? 97. How many perches in length, with 12 in breadth, must I receive in exchange for 40 perches in length and 18 in breadth? 98. There are two rooms, the floors of which have an equal number of square feet; the one is 50 feet by 30, the other is 40 in length: what is the breadth? 99. How many yards of paper, 3 quarters wide, will cover a chamber that is 60 feet round, and 10 feet 11 inches high? 100. How much stuff, 2 quarters wide, will face 15 yards of silk 3 quarters wide? 101. How many yards of brown drugget that is a yard and half wide, will cover a room that is 15 feet long and 14 broad? 102. If for a certain sum I can have 16cwt. 2qr. carried fifty miles, what distance would 66cwt. be carried for the same money? 103. A hare pursued by a greyhound was 86yds. before him at starting; whilst the hare ran 5yds. the dog ran 7yds. : how far had the dog ran when he caught the hare? 104. If 1.9703 acres cost $236.84, for how much can 874.695487 acres be purchased? THE DOUBLE RULE OF THREE. § 104. The double rule of three teaches to resolve questions which require to be stated more than once by the single rule of three. RULE. Put in the third place the term which is of the same kind as the answer. Proceed with each pair of terms exactly as in the single rule of three. Multiply all the first terms together for a general first term, and all the second terms together for a general second term. Multiply the second and third terms together, and divide by the first. EXAMPLES. 1. If 4 men earn $12 in 7 days, how long will 14 men be earning $30? Thus, draw a line and placing all the first terms below it, and all the second and third terms above it, and dividing any of them, of opposite sides, by any number which will divide 4×30×7 both without a remainder, as 9 14x12 the numbers 14 and 4 being both divisible by 2 without a remainder, will be reduced to 7 and 2; and 12 and 30 being divisible by 6, will be reduced to 2 and 5. The 7 above and the 7 below the line being on opposite sides, destroy each other, as do also the 2 above and the 2 below. The only remaining figure 5 will therefore be the answer. 2. A cellar which is 22.5 feet long, 17.3 wide, and 10.25 deep, being dug in 21 days, by 6 men, working 12.3 hours a day: how many days of 8.2 hours, should 9 men take to excavate one which measures 45. by 34.6 by 12.3 feet? 3. If 507. in of a year gain 21. 5s. 1d. 2 gr., in what time will 137. gain 17., and at what rate per cent. per annum ? |