makes after, at the rate of 40 rods a minute; how long will the course hold? and what distance will the dog run? Ans. 144 minutes, and he will run 570 rods 83. The hour and minute hands of a watch are exactly together at 12 o'clock; when are they next together? In 1 hour the minute hand passes over 12 spaces, and the hour hand over 1 space; that is, the minute hand gains upon the hour hand 11 spaces in 1 hour; and it must gain 12 spaces to coincide with it. Ans. 1 h. 5 m. 27 † & 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 over take 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 1871 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 rate per gallon must he sell it? Ans. $2'936+. 88. Thomas sold 150 pine apples at $334 apiece, and received as much acney 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, += 1 of the 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: I's of the pupils study grammar, geography, arithmetic, learn to write, and 9 learn to read: what is the number of each? 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 2 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 of the required numAns. 80. ber. 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++++= times the required number. Ans. 48, 100. What number is that, which, being increased by and of itself, and by 22 more, will be made three times us much? The number, being taken 1, 2, 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 ? Ans. A 12 years, B 18 years, C 63 years old. 103. A schoolmaster, being asked how many scholars he bad, 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 g, that is, of the stock, is equal to 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 $27'50; how many days did he work, and how many was he idle? Had he worked every day, his wages would have been $75 × 50 = $37'50, 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. 108. 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 8 years finds himself $40 in debt; what is their income, and what does each spend per annum? Ans. Their income, $200 per annum; A spends $175, and B $205 per annum. 107. A man, lying at the point of death, left to his three sons his property; to A wanting $20, to B, and to C 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? much to fill 2 of each sort? sort? how - how much to fill 6 of each 117. A man would draw off 30 gallons of wine into I nint and 2 pint bottles, of each an equal number; how many bottles will it take, of each kind, to contain the 30 gallons? Ans. 80 of each 118. A merchant has canisters, some holding 5 pounds, some 7 pounds, and some 12 pounds; how many, of each an equal number, can be filled out of 12 cwt. 3 qrs. 12 lbs. of tea? Ans. 60. 119. If 18 grains of silver make a thimble, and 12 pwts. make a teaspoon, how many, of each an equal number, can be made from 15oz. 6 pwts. of silver? Ans. 24 of each. 120. Let 60 cents be divided among three boys, in such a manner that, as often as the first has 3 cents, the second shall have 5 cents, and the third 7 cents; how many cents will each receive? Ans. 12, 20, and 28 cents. 121. A gentleman, having 50 shillings to pay among his labourers for a day's work, would give to every boy 6 d., to every woman 8 d., and to every man 16 d.; the number of boys, women, and men, was the same; I demand the number of each. Ans. 20. 122. A gentleman had 7 £. 17 s. 6 d. to pay among his labourers; to every boy he gave 6 d., to every woman 8 d., and to every man 16 d.; and there were for every boy three women, and for every woman two men; I demand the number of each. Ans. 15 boys, 45 women, and 90 men. 123. A farmer bought a sheep, a cow, and a yoke of oxen for $82'50; he gave for the cow 8 times as much as for the sheep, and for the oxen 3 times as much as for the cow; how much did he give for each? Ans. For the sheep $2'50, the cow $20, and the oxen $60. 124. There was a farm, of which A owned, and B, the farm was sold for $1764; what was each one's share of the money? Ans. A's $504, and B's $ 1260. 125. Four men traded together on a capital of $3000, of which A put in, B, C, and D ; at the end of 3 years they had gained $2364; what was each one's share of the gain ? Ans. A's 1182. S B's $1591. C's $ 394 126. Three merchants accompanied; A furnished of the capital, B, and C the rest; they gain $1250; what |