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who is to travel at the rate of 4 miles an hour, without intermission. At 3 o'clock in the afternoon of the same day, a messenger leaves Pittsburgh for this town, who is to travel at the rate of 7 miles an hour. Whereabouts on the road will they meet? Ans. The messenger from Washington will meet the
messenger from Pittsburgh, 59 miles from Washington; and the messenger from Pittsburgh will meet the messenger from Washing
ton, 40,2 miles from Pittsburgh. 43. A and B are on opposite sides of a circular field, 300 rods about: they begin to go round it at the same time, and the same way. A goes 22 rods in two minutes, B 34 rods in three minutes. How many times will they go round the field, before B overtakes A ? Ans. 17 times round.
44. A water tub holds 100 gallons; the pipe which conveys the water to it, adınits 7 gallons in 5 minutes, and the tap discharges 20 gallons in 17 minutes. Now supposing both of these to be left open intentionally, and the water to be turned on at 4 o'clock in the morning, a servant, at 6 o'clock, observes the water running, and puts in the tap. In what time after this accident will the tub be full ?
Ans. 51111 min. past 6 o'clock. 45. A gay young fellow soon got the better of of his fortune: he then gave 6000 dollars for a commission in the army, and continued his extravagancies till he had but 1800 dollars left, which he found to be but of his njoney, after he had purchased his commission. What was his fortune at first?
Ans. 15120 dollars. 46. Suppose a bar of steel to weigh 12 lbs. in one scale, and in another 10 lbs. what is the true weight of the steel?
Ans. 10,954 lbs. 47. A merchant was possessed of } of a ship, and sold of his interest for 1500 dollars. I demand the full amount of the ship, at that rate?
Ans. 6000 dollars. 48. In an orchard of fruit-trees, # of them bears pears, apples, plums, and 50 of them peaches, and 30 of them cherries. How many trees are in the orchard of all sorts ?
Ans. 960 trees. 49. A, B and C, have among them 200 dollars. A's and B's is to B's and C's as 5 to 7; and C's, less B's, is to C's and B’s as 1 to 7. How inany dollars had each of them?
Ans. A had $44, B 866%, and C 8889. 50. In a series of proportional numbers, the first is 4, the third is 12, and the product of the second and third is 112,8. I demand the difference of the second and fourth?
Ans. 18,8 differencer
51. There is an island 40 miles in circumference, and three men start together to travel round it: A goes 7 miles a day, B 8, and C 9. When will they all come together? Ans. In 40 days; and A will travel 280 miles, B 320
miles, and C 360 miles. 52. What number is that, from which, if you take 4, the remainder will be ?
53. A gentleman making his addresses in a lady's family, who had five daughters, she told him that their father had made his will, which imported, that the first four of the girls' fortune together was 20000 dollars, the last four was 26400 dollars, and the three last, with the first, was 24000 dollars; and the three first, with the last, made 22400 dollars, and the two first, with the two last, was 25600 dollars, which, if he could unravel, and make appear what each is to have, as he had a partiality for Charlotte, the second daughter, he should be welcome to her. What was her fortune, and that of each separately? Ans. First daughter's fortune was $3200, Charlotte's
was 85600, third daughter's, $ 4000, fourth
daughter's, 87200, fifth daughter's, 89600. 54. Being 16 miles 4 furlongs from Baltimore, I saw with my telescope, in the dusk of the evening, the lamp of the lighthouse in the horizon, at which time my eye was six feet above the surface of the water. What is the height of the lighthouse above the water? Ans. 43 yards nearly.
55. A, B and C, found a purse of money, containing 234 dollars, and agreed to have it so divided, that when X’s is multiplied by 2, B’s by 3, and C's by 4, their products will be alike. I deinand each man's share of the money?
Ans. A's share $108, B's $72, and C's 854. 56. A gambler loses, in four turns of dice, 320 dollars, and tripled each turn the sum he put in. I demand how much he played for the first and last time?
Ans. $8 the first time, and 8216 the last time. 57. If a bear can eat a goose in 10 minutes, a wolf in 20 mninutes, and a fox in 40 minutes, how long would they all be in eating it, if let at it together? Ans. 5 min. 42 sec.
58. Divide 20 dollars between four persons, giving one the third, another the fourth, another the fifth, and the fourth man one-sixth. What is each man's share ? Ans. The first got 737, the second 534, the third 4*,
and the fourth 3 dollars. 59. When half the number of an assembly, and 20, were met, there were a third and 10 absent. How
did the branch of the legislature consist of? Ans. 180 members.
60. If three unequal vents will severally empty a vessel of 120 gallons in one hour, two hours, and three hours, in how long would they empty it, if all running at once?
Ans. 32 min. 4311 sec. 61, What weight of lead will cover a house, the area of whose roof is 6000 feet, and the thickness of the lead to part of a foot?
Ans. 15 tons 15 cwt. 3 qrs. 26 lbs. 10 oz. 62. Suppose the length of a sluice to be 30 feet, and the depth of water 4 ft. 6 inc. I demand the pressure against the side of the sluice? (See page 207.)
Ans. 7 tons 10 cwt. 2 qrs. 19 lbs. 63. Suppose a vessel 3 feet wide, 5 feet long, and 4 feet deep, I demand the pressure on the bottom of that vessel, it being filled with water to the brim? (See page 207.)
Ans. 1 ton 13 cwt. i qr. 26 lbs. 64. If a stream of clear water moves at the rate of 100 yards per minute, and meets with a fixed obstacle, 20 feet wide, and 3 feet high, I demand the momentary pressure of the stream? (See page 207.)
Ans. 73121 lbs. Note. Water loses two-thirds of its power, in producing effects, being a yielding substance.
65. Let the squares of two numbers be 3161, (that is, their sum,) and their half sum, 15601. I demand those numbers ?
Ans. Greater 44, lesser 35. 66. Suppose the velocity of a cannon-ball to be 600 feet per second, I demand from what height must a body fall, to : acquire the same velocity ?
Ans. 5625 feet. 67. If the diameter of a round stick of timber be 24 inc., from end to enl, and its length 20 feet, I want to know how many solid feet it will contain, after it is hewn square, and what will be the contents of the slabs, which reduced it to. a square? Ans. 40 feet the contents, when squared.
22,8 feet the contents of the slabs. 68. If a round stick of timber, 9 inches in diameter, con.. tains 5 solid feet, I demand the diameter of one such stick, of the same length, which will contain ten times as much
Ans. 28,46 inches. 69. Suppose I am getting a chaise made, and direct that t'ie length of the shafts, between the axle-tree and backband, be 8 feet, and a dispute arises, wliereabouts on the shafts the centre of the body should be fixed. The chaise-maker advised to place it 30 inches before the axle-tree, but others supposed 20 inches would be a sufficient encumbrance for the horse. Now supposing two passengers to weigh 336 lbs.
and the body of the chaise 84 lbs. more, I demand what will the horse bear in both cases more than his harness?
Ans. By the chaise-maker's directions, 1314 lbs.
By the by-standers' directions, 874 lbs. 70. A, B and C, can do a piece of building in 15 days: A can finish or do it in 30 days, and B in 40 days. Idemand in what time can C finish it alone? Ans. 120 days.
71. A and B can finish a piece of work in 20 days, and with C they can do it in 12.' In what time can C do it by himself?
Ans. So days. 72. If tea is sold at 1 dol. 20 cts. which cost 1 dol. 25 cts. a pound, what is the loss per cent.? Ans. 4 per cent.
73. If by selling a yard of cloth for 2 dollars 30 cents, I gain 15 per cent. what would I gain per cent. by selling the same cloth at 2 dollars 40 cents per yard?
Ans. 20 per cent. 74. There are two numbers, whose product is 1610; the greater is 46. What is the sum of their squares, and what the cube of their difference?
Ans. 3341 the sum of their squares.
1331 the cube of their difference. 75. There is a mast or pole, ş of whose length stands in the ground, 12 feet of it in the water, and of its length in the air, or over water. I demand the whole length ?
Ans. 216 feet. 76. There are two pieces of linen, one of which is 9 yards shorter than the other, and cost 12 dollars 24 cents: the other piece at the same price cost 14 dollars 40 cents. I demand how many yards are in both pieces, and the price of one yard?
Ans. 111 yds. in both pieces.
24 cents per yard. 77. In 81034 kilderkins of wine, each 18 gallons, how many gross of bottles, each of a quart?
Ans. 45581 gross 7} dlozen. 78. Col. Beatty, of Cambridge, Ohio, being desirous to know how much money the toll of Cambridge bridge would amount to in a certain time, gave orders to David Ballan. tine, to receive of every wagon 25 cents, of every
horseman 12 cents, and of every footman 64 cents. Now, at the end of the year, Ballantine brings his account to Col. Beatty, amounting to 1325 dollars, and tells him, that as often as 5 passed with wagons, 9 passed on horseback, and as often as 6 passed on horseback, 10 passed on foot. I demand how many passed with wagons, how many on horseback, and on foot? Ans. 2000 wagons, 3600 horsemen, 6000 footmen,
79. Five merchants, A, B, C, D and E, have gained 2000 dollars, which they divide in such a way, that į the share of A is equal severally to 1 of B’s, of C's, I of D's, and of
What was each merchant's share ?
Ans. A's $160, B's 320, C's 400, D's 480, E's 640. 80. Twenty admirals, 30 post-captains, 24 sailing-masters, and 24 lieutenants, spent 256 dollats at a ball, which sum was divided in such a manner, that 4 admirals paid as much as 5 post-captains, and 10 post-captains as much as 16 sailing-masters, and 8 sailing-masters as much as 12 lieutenants. I want to know the sum of money paid by the admirals, post-captains, sailing-masters, and lieutenants ? Ans. The 20 admirals paid $80, the 30 post-captains
896, the 24 sailing-masters 848, and the 24
lieutenants $32. 81. A, B and C, will make 20 rods of the turnpike road in 12 days; B, C and D, in 14 days; C, D and A, in 15 days; and D, A and B, in 18 days. In what time will it be done by all of them working together, and by each singly? Ans. By A in 47,848 days, by B in 38,969 days, by C
in 27, 194 days, by D in 111,176 days, and by
A, B, C and D, in 10,8309505 days. 82. Suppose A and B to have between them a certain number of dollars, to be so divided, that the sum of their squares may be 208, and the difference of their
80. Now supposing A to have the greater quantity, how many had be more than B?
Ans. A had 4 more than B; A's number 12, B's 8. 83. Bar Chad 50 dollars between them, which was to be so divided, that the sum of their squares should be 1300 dollars. How many had each, supposing B to have the greater quantity? Ans. B had 30, and C 20 dollars.
84. Divide 316 dollars 96 cents between 4 men, 6 wo• men, and 9 boys, giving each man as much as two women, and each woman as much as two boys.. What is each of their shares ? Ans. Each man got 34 dollars 26 cents, each woman
17 dolls. 134 cts. and each boy 8 dolls. 564 cts. 85. What two numbers being added will make 2663, and when one is multiplied by 3, and the other by 5, their products will be equal ?
Ans. 1669 and 100. 86. A man married a wife, and when the wedding day came, he was just double her
age. After they had lived together 30 years, his age was in proportion to her's, as