74. If a man earn $1.15 in of a day, how much can he earn in of a day? (See example 25.) 75. Suppose of an acre of land to be worth 54 dollars; what is į of an acre worth? To solve this question, by the process to which the scholar has been led, he will consider à as a denominator and as the numerator of a complex fraction, expressing what part of 54 dollars į of an acre is worth; and, after reducing this complex fraction to a simple one, will multiply the simple fraction into 54 dollars, for the answer. Now the effect of the process is the same as that of multiplying the 54 by, and dividing the product by; and this last method is to be preferred, because it is shorter. Thus, 54X1=6, and 6==8. 76. If of a ship cost $15000, what does of her cost? 77. If į of a lot of new land be worth 300 dollars, what is 7 of the lot worth? 78. If a horse trot 1840 rods in 18 of an hour, how many rods does he trot in 5 of an hour ? 79. If 964 yards of cloth cost $642, what will 28.16 yards cost,. at the same rate ? 80. If 15 yards of cloth cost $75, what will 1427 cost, at the same rate ? 81. If 9 barrels of flour be consumed by a company in 18 days, how long will 253 barrels last ? 82. If a mill grind 18 bushels of corn in 1 hour and 22 minutes, in what time will it grind 25bushels ? 83. If a ship sail 924 miles in 8 hours, in how many hours does it sail 65 miles ? 84. If a barrel of four will support 12 men for 25 days, how long will it support 8 men ? Since the flour will support 12 men 25 days, it would support 1 man 12 times 25 days, or 300 days; and since it would support 1 man 300 days, it will support 8 men i of 300 days, or 37 days. Thus, to obtain the answer, we multiply 25 days by 12, and divide the product by 8. A little attention to the conditions of this question, and the process of the operation, will enable the learner to perceive, at once, that the answer is of 25 days. 85. If a quantity of beef will support 436 men 73 days, how long will it support 240 men ? 86. If a barrel of beer will last 10 men 16 days, how long will it last 23 men ? The beer would last 1 man 10 times 16 days, or 60 days; and it will last 23 men 2 of 60 days, or 214 days =2 days. The question is, however, more conveniently viewed thus, - Since the beer will last 10 men 16 days, it will last 23 men 23 of 16 days; and, hence, 16 is to be multiplied by 87. Suppose a certain quantity of hay will feed 85 sheep 71 days; how long will it feed 230 sheep?. 88. If 256 men can make a certain piece of road in 240 days, in what time will 190 men make it ? 89. If 9 yards of silk, that is 3 quarters wide, will line a cloak, how many yards, that is 5 quarters wide, will line the same cloak ? 90. If 110 yards of paper, that is 32 inches wide, will cover the walls of a room, how many yards, that is 24 inches wide, will cover the same walls ? 91. Suppose a man can perform a piece.of work in 45 days, by working 7 hours a day, in what time will he perform it, if they work 10 hours a day? 92. Suppose a company of men can perform a piece of work in 155 days, by working 12 hours a day, in what time will they perform it, by working 5 hours a day? 93. How many days will it take 119 horses to eat the hay that 44 horses would eat in 60 days ? 94. The hind wheels of a coach, which are 180 inches in circumference, will turn round 4825 times in running a certain distance, how many times will the forward wheels turn round, they being 145 inches in circumference? 95. If a ship, by sailing 9 miles an hour, will effect a passage to Europe in 55 days, in how many days would she effect the passage by sailing 13 miles an hour ? 96. If a vessel, by sailing 10 miles an hour, will make a passage from Bangor to New Orleans in 11 days, in how many days would she make the passage by sailing 12 miles an hour ? 97. Suppose A rides 67 miles an hour, and performs a certain journey in 14 days; in what time will B, who rides only 41 miles an hour, perform the same journey? 98. If 6 persons expend $ 300 in 3 months, how much will serve 15 persons for 20 months ? Since 6 persons expend $ 300 300 750 in 8 months, 15 persons would, 15 20 in the same time, expend of 815000 $300, which is $750. Then, since 15 persons would expend 750 1875 $750 in 8 months, they would, in 20 months, expend of $750, which is $1875. The adjoined operation corresponds to this solution. 99. If the wages of 6 men for 14 days be $ 84, what will be the wages of 9 men for 11 days ?. 100. If 3 pounds of yarn make 9 yards of cloth, 5 quarters wide, how many pounds would be required to make a piece of cloth 45 yd. long and 4qr. wide ? 101. If a class of 25 girls perform 1750 examples in arithmetic, in 15 hours, how many examples of equal length may a class of 30 girls perform, in 13 hours ? 102. If the use of $ 100 for 90 days, be worth $1.50, what is the use of $78 for 85 days worth? 103. If the use of $ 100 for 30 days be worth 75 cents, what is the use of $ 1240 for 57 days worth? 104. If a man travel 217 miles in 7 days, travelling 6 hours a day, how many miles will he travel in 9 days, if he travel 11 hours a day? When he travels 6 hours a day, he advances 217 miles in 7 days, and were he to proceed thus for 9 days, he would advance of 217 miles, or 279 miles. Since, by travelling 6 hours a day he would, in 9 days, advance 279 ml., by travelling 11 hours a day, he would advance ☺ of 279 ml., which is 211 ml., or 2113 ml. 105. If a man perform a journey of 1250 miles in 15 days, by travelling 14 hours a day, how many days will it take him, to perform a journey of 1000 miles, by travelling 13 hours a day? 106. If 10 cows eat 7 tons of hay in 14 weeks, how many cows will eat 22 tons in 28 weeks ? 105 a day; hours a dhours a day.eed thusiles. Sin 107. If 6 men will mow 35 acres of grass in 7 days, by working 10 hours a day, how many men will be required to mow 48 acres in 5 days, when they work 12 hours a day? 108. If 14 men can cut 87 cords of wood in 3 days, when the days are 14 hours long, how many men will cut 175 cords, when the days are 11 hours long? 109. If 16 men can build 18 rods of wall in 12 days, . how many men must be employed to build 72 rods of the same kind of wall in 8 days ? 110. If 25 persons consume 600 bushels of corn in 2 years, how much will 139 persons consume in 7 years ? Since 25 persons consume 600 bushels in 2 years, 139 persons would, in the same time, consume 13 of 600 bushels, which is 3336 bushels. Then, since 139 persons would consume 3336 bushels in 2 years, they will, in 7 years, consume of 3336 bushels, which is 11676 bushels. 111. If 154 bushels of oats will serve 14 horses for 14 days, how long will 406 bushels serve 7 horses ? 112. If 25 men can earn $ 6250 in 2 years, how long will it take 5 men to earn $11250 ? 113. If 9 men can mow 36 acres of grass in 4 days, how many acres will 19 men mow in 11 days ? 114. If a family of 9 persons spend $ 450 in 5 months, how much would be sufficient to maintain the family 8 months, after 5 more persons were added ? 115. If a stream of water running into a pond of 190 acres, will raise the pond 10 inches in 12 hours, how much would a pond of 50 acres be raised by the same stream, in 10 hours ? 116. If the wages of 4 men, for 3 days, be $11.04, how many men may be hired 16 days for $103.04? 117. If 3 men receive £8 18s. for working 19 days what must 20 men receive for working 1004 days ? 118. If 1112 bottles are sufficient to receive 5 casks of wine, how many bottles are sufficient to receive 13 casks of wine ? | 119. If 725 bottles hold 4 barrels of wine, how many bottles are required to hold 3 tierces of wine ? 120. If 240 men, in 5 days, of 11 hours each, can dig a trench 230 yards long, 3 yards wide, and 2 yards deep, in how many days, of 9 hours each, will 24 men dig a trench 420 yards long, 5 yards wide, and 3 yards deep? Since 248 men, in 5 days, of 11 hours each, can dig a trench 230 yards long, 3 yards wide, and 2 yards deep, 24 men, working in days of the same length, would dig a trench of the same dimensions in 24 of 5 days, which is 512=51} days; and, working in days of 9, instead of 11 hours each, the trench would occupy them 1 of 51 days, which is 637 days. Again, since the trench to be dug by 24 men is 420, instead of 230 yards long, this length, (the width and depth remaining unchanged) would occupy them 230= of 637 days, which is 1152067 days. Again, since the trench to be dug by 24 men is 5, instead of 3 yards wide, this width (the depth remaining unchanged) would occupy them z of 115.25 days, which is 192711 days. Lastly, since the trench to be dug by 24 men is 3, instead of 2 yards deep, it will occupy them of 192721 days, which is 283727=2887207 days, the answer 121. If 12 men can build a brick wall 25 feet long, 7 feet high, and 4 feet thick, in 18 days, in how many days will 20 men build a brick wall 150 feet long, 8 feet high, and 5 feet thick ? 122. If 15 men can dig a trench 75 feet long, 8 ft. wide, and 6 ft. deep, in 12 days, how many men must be employed to dig a trench 300 ft. long, 12 ft. wide, and 9ft. deep, in 10 days ? 123. If the carriage of 44 barrels of flour, 108 miles be worth $215, what is the carriage of 36 barrels, 162 miles worth? 124. If 175 bushels of corn, when corn is worth 60, cents a bushel, be given for the carriage of 100 barrels of flour, 58 miles, how many bushels of corn, when corn is worth 75 cents a bushel, must be given for the carriage of 90 barrels of flour, 200 miles ? 125. If 12 ounces of wool make 21 yards of cloth, that is 6 quarters wide, how many pounds of wool would make 150 yards of cloth, 4 quarters wide ? |