2 to 14; and 30 years after, his age was to her's, as 2 to 13: then they both died. I demand their different ages? Aus. His age 40 years, and her's 20, when married. When they had lived together 30 years, his age was 70 yrs. and her's 50, making his age to her's, as the proportion of 2 to 13: and 30 years after that, his age was 100 years, and her's 80, making a proportion of his to her's, as 2 to 13. 87. The hour and minute hands of a watch or clock, are together precisely at 12 o'clock: when are they next together P Ans. At 5 min. 273 sec. past 1 o'clock, at 10 minutes 54 sec. past 2 o'clock, at 16 min. 21 sec. past 3 o'clock, &c. 88. A number of dollars are to be divided between two men, A and B, in such a manner, that A may have 50 more than B, and that the sum of the squares of their respective shares may be 12500 dolls. I demand each man's number? Ans. A had $100, and B 50. 89. Tom and Jack, playing at cards, having at first 14 dollars apiece, but after playing several games, Jack, having lost some of his, would play no longer; and it was found that the difference of the squares of the numbers that each then had, was 336. Pray how much did Jack lose? Ans. 6 dollars. 90. Said William to James, my father gave me 12 cents more than he gave my brother John, and the difference of the squares of our separate parcels is 288. Now tell how many he gave us each? Ans. William 18 cents, and John 6 cents. 91. On how much ground do 2016 soldiers stand, by placing 56 in rank, and 36 in file, and to stand 4 feet distance in rank, and the same in file? Ans. 30800 square feet. 92. I want to plant an orchard of 600 apple-trees, so that the length shall be to the breadth, as 3 to 2; and the distance of each tree, one from another, may be 7 yards. How many trees must be in length, how many in breadth, and how many square yards of ground do they stand on? Ans. 30 in length, and 20 in breadth, and standing on 26999 square yards. 93. If a pipe, 6 inches bore, will discharge a certain quantity of water in 4 hours, in what time will 3 pipes, each 4 inches, discharge double as much water? Ans. 6 hours. 94. Suppose a ladder 60 feet long be so placed, as to reach a window 37 feet from the ground, on one side of the street, and by moving or turning the ladder, (not at the foot,) over, will reach a window 28 feet high, on the other side of the street. What is the breadth of the street? Ans. 102,64 feet. 95. Suppose a boat should set out from Wheeling, to go down the river 20 miles, and another boat start 20 miles below Wheeling, to come up the river to Wheeling, at the same moment of time; and suppose the current forwards one, and retards the other a mile and a half an hour. The boats are equally laden, and the rowers equally good, and in the common way of rowing in calm water, each would proceed at the rate of four miles an hour. How far from Wheeling will the two boats meet? Ans. The boat from Wheeling will meet the boat going to Wheeling 133 miles below Wheeling, and the boat going to Wheeling will then be 64 miles from where she started. 96. I want to know how long a blacksmith would make a rod, or bar of iron, fourth of an inch square, out of a solid foot of iron, allowing no waste for the fire ? Ans. 576 feet long. 97. A country spark paid his addresses to a young lady versed in numbers, and asked her age, to which she replied, that if her age was multiplied by 3, and of that product tripled, the square root of of that product will be 4. Now kind sir how old am I? Ans. 14 years. 98. What are those two numbers, whose sum is 48, and their difference 14? Ans. 31 and 17. 99. Suppose a tavern signpost to be 40 feet above the surface of the ground, and it was observed to incline to fall, occasioned by the wind blowing hard, one foot from the topend in 24 hours, and the next 24 hours one foot more, and so on, every 24 hours one foot, until such time as it lay flat on the level ground. How long was the signpost in falling, Ans. 62 days 20 hours 342 minutes. at that rate? 100. William Rabe, merchant of this town, (Washington, Guernsey county, Ohio,) has engaged three horses, belonging to different men, A, B and C, to haul a load of tobacco to Wheeling, for ten dollars. A and B are supposed to haul of the load, and A and C B and C can haul of the load. They are to be paid according to their work. How much is each to get of the ten dollars? 4715 4715 Ans. A is to get 4 dolls. 2139 cts. B 3 dolls. 94,290 cents, and C I dollar 841440 cents. 101. The same merchant, William Rabe, bought three horses from different men for 200 dollars; one of them from Jacob Endley, one from Samuel Laurence, and one from William Skinner. They were to be paid for according to their several abilities in hauling, and in order to determine their prices, they were proved in the following manner: Jacob Endley's horse hauled a certain load of salt, from Cambridge to Washington, in ten hours. Jacob Endley's horse, and Samuel Laurence's horse, will haul the same quantity of salt from the same place in six hours. Jacob Endley's horse, and William Skinner's horse, will do the same work in four hours. Now I demand who owned the best horse, and the several prices paid to each owner? Ans. Wm. Skinner received 94 dolls. 73 cts. 615 m. Jacob Endley received 63 dolls. 15 cts. 717 m. Samuel Laurence rec'd. 42 dolls. 10 cts. 55 m. 102. Suppose a body to weigh 400 lbs. at 2000 miles distance above the surface of the earth, what would the same body weigh on or at the surface, estimating the earth's semidiameter at 4000 miles? Ans. 900 lbs. 103. If a body on the surface of the earth weighs 180 lbs. how high must it be raised in the air, to weigh only 20 lbs.? Ans. 8000 miles high. 104. How high will a rifle-ball, that runs 120 to a pound, go in the air, to lose half its weight? Ans. 1656,85 miles high. 105. A can finish a certain length of the national turnpike road in 13 days; A and B together in 8 days. In what time can B do it alone? Ans. 20 days. 106. A tract of land is to be laid out in form of an equal square, and to be enclosed by a fence of post and rails, of five high, so that each rod of fence shall contain ten rails. How large must the square be, to contain just as many acres of land as there are rails in the fence that encloses it, so that every rail shall fence an acre? Ans. 256000 rails, which encloses 256000 acres of land, and the ground or tract will be 20 miles square. 107. If 6 lbs. of pepper be worth 13 lbs. of ginger, and 19lbs. of ginger be worth 4 lbs. 12 oz. of cloves, and 10 lbs. of cloves be worth 63 lbs. of sugar, at 5 cents a pound, what is the value of 100 lbs. of pepper? Ans. 17 dollars 6 cents. 108. If when wine is 70 dollars per hogshead, a company of 45 persons will spend 80 dolls. therein, in a certain time, what is the wine a pipe, when 13 persons more will spend 252 dollars in twice the time, drinking with equal moderation ? Ans. 171 dollars 7 cents nearly. 109. William Rabe despatches his clerk from Washington to Philadelphia, distant 400 miles, with orders to purchase goods, his route fixed at 22 miles a day. Four days after, he sent a messenger after him with fresh orders, and is to travel at the rate of 32 miles a day. How many miles this side of Philadelphia will the messenger overtake the clerk ? Ans. 118 miles. 110. A merchant sold cloth at 2 dollars 20 cents a yard, by which he cleared of his money; but growing scarce, he raised the same cloth to 2 dollars 70 cents per yard. I demand his profit per cent. at the latter price? Ans. 96 dollars 36 cents per cent. 111. A man dying left his wife with child, and by his will ordered, that if she had a son, of the estate should belong to him, and the remainder to his mother: and if she had a daughter, the mother was to have, and the daughter. But it happened she was delivered of both a son and daughter, by which she lost in equity 8000 dollars more than if it had been only a girl. I demand how much would have been her dowry, if she had only a son? Ans. 7000 dolls. 112. A, B and C, put in a common stock 15440 dollars, to trade in company. A's was in 3 months, B's 5 months, and C's 7 months, and they gained 936 dollars, which was to be so divided, that of A's gain was equal to of B's, and of B's to of C's. I demand how much each put in stock, and each man's gain? Ans. A put in $5600, B 5040, and C 4800. A gained $208, B gained 312, and C gained 416. 113. A man married a wife, and on his wedding day, his age was to his wife's age, as 3 to 1; and when they had lived together 15 years, his age then was to his wife's age, as 2 to 1. I demand both their ages when married? Ans. He was 45, and his wife 15. 114. A father divided a sum of money between his three sons, A, B and C: he gave A 7 dollars as often as B 4; to Che gave 2 as often as B 5; and the dividend of C came to 2000 dollars. What was each son's share, (that is, A's and B's,) and the whole legacy? Ans. A's share was $8750, B's 5000, C's 2000, and the whole legacy was $15750. 115. Suppose in a room, where two men are sitting, A and B, there is a fire, from which A is 3 feet, and B 6 feet distant: it is required to find how much hotter it is at A's seat, than at B's? Ans. A is 4 times as warm as B. 116. Suppose the battering ram, used by the Turks, to weigh 8000 lbs. that it was moved 24 feet in a second, and that was sufficient to demolish the walls of with what velocity must a cannon-ball be moved, which weighs 42 lbs. to do the same execution ? 6. Ans. 45713 feet in a second. 117. What quantity of water must be added to a pipe of wine, which cost 132 dollars, to reduce the first cost to 90 cents per gallon? Ans. 203 gallons of water. 118. A man caught a fish, whose head was 8 inches long, and the tail as long as the head and half the body, and the body was just as long as the head and tail. What was the length of the fish? Ans. 64 inches. 119. Two merchants enter into partnership, each of them putting in 8 hhds. of tobacco, those of A costing 192 dollars more than B's. The tobacco being sold, they find they have gained 1000 dollars, of which B had, for his share, 450 dolfars. The question is to know, at how much was each parcel of tobacco valued ? Ans. A's valued at $132, and B's at $108 per hhd. 120. If rum is sold at 50 dollars a hogshead, and there is lost 6 per cent. how much is the gain or loss, when 4 hhds. are sold for 180 dollars? Ans. 15 dollars 39 cents per cent. loss. 121. What sum of money, at 3 per cent. per annum, will clear 154 dolls. in 1 year and 8 months? Ans. $3520. 122. Having a desire to collect a number of men for a frolick, and wishing to keep them sober, I had a barrel containing 32 gallons of whiskey, out of which I took 5 gallons, and replaced it by putting in 5 gallons of water; and finding it too strong, took out 5 gallons more, putting in 5 gallons of water, and did so five times altogether, still minding to replace the 5 gallons taken out, by 5 gallons of water. I demand the quantity of whiskey and water in the barrel? Ans. 1377 gallons of whiskey, and 18,33117% gallons of water. 1048 1048576 123. What number is that, which being divided into four or five equal parts, the product of all the parts, in both cases, shall be exactly the same? Ans. 12 53 124. Bought a certain quantity of cloth for 2400 dollars; and if the number of dollars it cost per yard was added to the number of yards bought, the sum would be 604. I demand the number of yards bought, and at what price per yard? Ans. 600 yards, at 4 dollars per yard, |