by a pipe which iets in 7 gallons in 5 minutes; but there is a leak in the bottom of the cistern which lets out 2 gallons in 6 minutes; supposing the cistern empty, in what time would it be filled? In 1 minute of a gallon is admitted, but in the same time of a gallon leaks out. Ans. 6 hours, 15 minutes. 74. A ship has a leak which will fill it so as to make it sink in 10 hours; it has also a pump which will clear it in 15 hours now, if they begin to pump when it begins to leak, in what time will it sink? In 1 hour the ship would be the same time it would be filled by the leak, but in emptied by the pump. Ans. 30 hours. 75. A cistern is supplied by a pipe which will fill it in 40 minutes; how many pipes, of the same bigness, will fill it in 5 minutes ? Ans. 8. 76. Suppose I lend a friend $500 for 4 months, he promising to do me a like favour; some time afterward, I have need of $300; how long may I keep it to balance the former favour? Ans. 6 months. 77. Suppose 800 soldiers were in a garrison with provisions sufficient for 2 months; how many soldiers must depart, that the provisions may serve them 5 months? Ans. 480. 78. If my horse and saddle are worth $84, and my horse be worth 6 times as much as my saddle, pray what is the value of my horse? Ans. $72. 79. Bought 45 barrels of beef, at $3'50 per barrel, among which are 16 barrels, whereof 4 are worth no more than 3 of the others; how much must pay? Ans. 143'50. 80. Bought 126 gallons of rum for $110; how much water must be added to reduce the first cost to $75 per gallon? Note. If $75 buy 1 gallon, how many gallons will $110 buy? Ans. 20 gallons. 81. A thief, having 24 miles start of the officer, holds his way at the rate of 6 miles an hour; the officer pressing on after him at the rate of 8 miles an hour, how much does he gain in 1 hour? how long before he will overtake the thief? Ans. 12 hours. 82. A hare starts 12 rods hefore a hound, but is not perceived by him till she has been up 14 minutes; she scude away at the rate of 36 rods a minute, and the dog, on view, makes after, at the rate of 40 rods a minute; how long will In 1 hour the minute hand passes over 12 spaces, and the 84. There is an island 20 miles in circumference, and three men start together to travel the same way about it; A goes 2 miles per hour, B 4 miles per hour, and C 6 miles per hour; in what time will they come together again? Ans. 10 hours. 85. There is an island 20 miles in circumference, and two men start together to travel around it; A travels 2 miles per hour, and B 6 miles per hour; how long before they will again come together? B gains 4 miles per hour, and must gain 20 miles to overtake A; A and B will therefore be together once in every 5 hours. 86. In a river, supposing two boats start at the same time from places 300 miles apart; the one proceeding up stream is retarded by the current 2 miles per hour, while that moving down stream is accelerated the same; if both be propelled by a steam engine, which would move them 8 miles per hour in still water, how far from each starting place will the boats meet? Ans. 112 miles from the lower place, and 187 miles from the upper place. 87. A man bought a pipe (126 gallons) of wine for $275; he wishes to fill 10 bottles, 4 of which contain 2 quarts, and 6 of them 3 pints each, and to sell the remainder so as to make 30 per cent. on the first cost; at what ráte per gallon must he sell it? Ans. $2936+. 88. Thomas sold 150 pine apples at $334 apiece, and received as much money as Harry received for a certain number of watermelons at $25 apiece; how much money did each receive, and how many melons had Harry? Ans. $ 50, and 200 melons. 89. The third part of an army was killed, the fourth part taken prisoners, and 1000 fled; how many were in this army? This and the eighteen following questions are usually wrought by a rule called Position, but they are more easily solved on general principles. Thus, += of the 1 army; therefore, 1000 is of the whole number of men; and, if 5 twelfths be 1000, how much is 12 twelfths, or the whole?" Ans. 2400 men. 90. A farmer, being asked how many sheep he had, answered, that he had them in 5 fields; in the first were of his flock, in the second, in the third, in the fourth, and in the fifth 450; how many had he ? Ans. 1200. 91. There is a pole, of which stands in the mud, in the water, and the rest of it out of the water; required the part out of the water. Ans. 92. If a pole be in the mud, g in the water, and 6 feet out of the water, what is the length of the pole? Ans. 90 feet. 93. The amount of a certain school is as follows: of the pupils study grammar, arithmetic, learn to write, and 9 learn to read: what is the number of each? geography, Ans. 5 in grammar, 30 in geography, 24 in arithmetic; 12 learn to write, and 9 learn to read. 94. A man, driving his geese to market, was met by another, who said, "Good morrow, sir, with your hundred geese;" says he, "I have not a hundred; but if I had, in addition to my present number, one half as many as I now have, and 21 geese more, I should have a hundred:" how many had he? 100 24 is what part of his present number? Ans. He had 65 geese. 95. In an orchard of fruit trees, of them bear apples, pears, plums, 60 of them peaches, and 40, cherries; how many trees does the orchard contain? Ans. 1200. 96. In a certain village, of the houses are painted white, red, yellow, 3 are painted green, and 7 are unpainted; how many houses in the village ? Ans. 120. 97. Seven eighths of a certain number exceed four fifths of the same number by 6; required the number. -; consequently, 6 is = ber. of the required numAns. 80. 98. What number is that, to which if of itself be added, the sum will be 30? Ans. 25. 99. What number is that, to which if its and be added, + the sum will be 84 ? 84=1+1+= times the required number. Ans. 48. 100. What number is that, which, being increased by ƒ and of itself, and by 22 more, will be made three times much? The number, being taken 1, 4, and 3 times, will make 2✈ times, and 22 is evidently what that wants of 3 times. Ans. 30. 101. What number is that, which being increased by 2, and & of itself, the sum will be 234 ? Ans. 90. 102. A, B, and C, talking of their ages, B said his age was once and a half the age of A, and C said his age was twice and one tenth the age of both, and that the sum of their ages was 93; what was the age of each ? a Ans. A 12 years, B 18 years, C 63 years old. 103. A schoolmaster, being asked how many scholars he had, said, "If I had as many more as I now have, as many, as many, and as many, I should then have 435;" what was the number of his pupils ? Ans. 120. 104. A and B commenced trade with equal sums of money; A gained a sum equal to of his stock, and B lost $200; then A's money was double that of B's; what was the stock of each ? By the condition of the question, one half of, that is, of the stock, is equal to g of the stock, less $200; consequently, $200 is of the stock. Ans. $500. 105. A man was hired 50 days on these conditions,—that, for every day he worked, he should receive $75, and, for every day he was idle, he should forfeit $25; at the expiration of the time, he received $2750; how many days did he work, and how many was he idle? Had he worked every day, his wages would have been $75 X 50: $3750, that is, $10 more than he received; but every day he was idle lessened his wages $75+ $25 $1; consequently he was idle 10 days. Ans. He wrought 40, and was idle 10 days. 106. A and B have the same income; A saves of his; but B, by spending $30 per annum more than A, at the end of 3 years finds himself $40 in debt; what is their income, and what does each spend per annum? Ans. Their come, $200 per annum; A spends $175, and B $205 per annum. 107. A man, lying at the point of death, left to his three sous his property; to A wanting $20, to B, and to C MISCELLANEOUS EXAMPLES. T 119. 247 the rest, which was $10 less than the share of A; what was each one's share? Ans. $80,$50.and $70. 108. There is a fish, whose head is 4 feet long; his tail is as long as his head and the length of his body, and his } body is as long as his head and tail; what is the length of the fish? The pupil will perceive, that the length of the body is the length of the fish. Ans. 32 feet. 109. A can do a certain piece of work in 4 days, and B can do the same work in 3 days; in what time would both, working together, perform it? Ans. 14 days. 110. Three persons can perform a certain piece of work in the following manner: A and B can do it in 4 days, B and C in 6 days, and A and C in 5 days: in what time can they all do it together? Ans. 3 days. 111. A and B can do a piece of work in 5 days; A can do it in 7 days; in how many days can B do it? Ans. 174 days 112. A man died, leaving $1000 to be divided between his two sons, one 14, and the other 18 years of age, in such proportion, that the share of each, being put to interest at 6 per cent., should amount to the same sum when they should arrive at the age of 21; what did each receive? Ans. The elder, $546'153-; the younger, $453'846-+. 113. A house being let upon a lease of 5 years, at $60 per annum, and the rent being in arrear for the whole time, what is the sum due at the end of the term, simple interest being allowed at 6 per cent.? Ans. $336. 114. If 3 dozen pair of gloves be equal in value to 40 yards of calico, and 100 yards of calico to three pieces of satinet of 30 yards each, and the satinet be worth 50 cents per yard, how many pair of gloves can be bought for $4? Ans. 8 pair. 115. A, B, and C, would divide $100 between them, so as that B may have $3 more than A, and C $ 4 more than B; how much must each man have? Ans. A $30, B $33, and C $37. 116. A man has pint bottles, and half pint bottles; how much wine will it take to fill 1 of each sort? how much to fill 2 of each sort? how much to fill 6 of each sort? 117. A man would draw off 30 gallons of wine into 1 nint and 2 pint bottles, of each an equal number; how |