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When it is noon at Boston, what is the hour at these mountains ?
Ans. 8 minutes before 12. 32. Easton, Massachusetts, is 6° east longitude from Washington, and Circleville, Ohio, is 6° west from Washington. How many degrees of longitude are these towns apart? what is the hour at Circleville when it is noon at Easton; and what is the hour at Easton when it is 15 minutes past 6 P. M. at Circleville ? Ans. to last question, 3 minutes past 7, P. M.
33. A meteor was seen for a few moments at Washington, at 14 minutes past 9 o'clock, P. M. It was also seen at Paris, Kentucky, which is 7° west, and at Easton 6° east from Washington. What was the time of the meteor's appearance at Paris and at Easton ? Ans. at Paris 46 m. past 8, P. M.; at Easton 38 m. past 9, P. M.
34. A vessel, named the Hamilton, sailed from New York to China, by way of the Cape of Good Hope, and thence to the Sandwich Islands, where she arrived on a Saturday morning by her reckoning. About an hour after her arrival, the Louisa, another vessel from New York came into the harbor, having come by way of Cape Horn. What day was it by the Louisa's reckoning, supposing both vessels to have kept the days of the week correctly?
Ans. Friday. 35. What would be the length of the day (i. e.,
from noon to noon) on board a steamship bound from New York to Liverpool, supposing her to traverse exactly 5° of longitude daily; and what would be the length of the day on board, returning, supposing her to traverse daily the same number of degrees of longitude? Ans. 23 h. 40 m.; 24 h. 20 m.
36. A merchant, dying, left a will devising as follows: to his wife $10,000; to each of his three sons $12,000; to each of his two daughters half that amount; to each of his three clerks $500; to his porter $100; the residue of his estate to be equally divided between his wife and daughters. His estate proved to be worth $75,000. How much did the wife and each daughter receive? Prove by trial.
37. A man owning of a ship sold of his share for $1875. How much was the whole ship worth at that rate ?
Ans. $30,000. 38. The cargo of a ship was valued at $37,230 and of the ship at $7500. What was the value of both ship and cargo?
Ans. $67,230. 39. A man having $100 purchased 4 cows, which took all the money he had except $28. How much did he pay apiece for them?
Ans. $18. 40. A farmer hired a boy for a year for $40 and a suit of clothes. But after he had stayed 5 months they agreed to part, the boy to receive full wages for the time he stayed. He received 6 dollars and the suit of clothes. How much money is left for 7 months' wages, and what were the clothes valued at?
Ans. to last question $18. 41. A mechanic hired a journeyman at 8 shillings and his board, for each day he worked ; but if he worked anywhere else, or was idle, the journeyman was to pay 5 shillings a day for his board. They settle at the end of fifty days, and the journeyman receives £10 18s. How many days did he work for the mechanic ?
Ans. 36 days. 42. A farmer brought a basket of eggs to market, and offered them for sale at 7 cents a dozen. A person
passing by stumbled against the basket and broke 5 dozen. Being paid for these, he resolved to sell the rest for 8 cents a dozen, by which he would receive as much as if he had sold the full number for 7 cents, besides the money for the broken eggs, which would then be clear profit. How much did he gain by raising the price? How many dozen must he have thus sold, then? How many dozen did he bring to market ? Prove by trial with the answer found.
43. A man brings eggs to market, and first sells 4 more than the half of them, then he goes further, and sells half the remainder and 2 over. Now 6 eggs more than half the remainder are stolen from him, and, dissatisfied with the loss, he returns home with the 2 eggs which remained in his basket. How many eggs had he at first? Prove by trial with the answer found.
44. I take a certain number, multiply it by 35, take 60 from the product, multiply the remainder by 23, and subtract 30, when nothing remains. What is the number? Prove by trial with the result.
45. Required two numbers, whose sum is 70, and whose difference is 16. If the sum is first divided equally, what process will make the one 16 larger than the other? Try. 46. Two purses together contain $300. If
take 30 out of the first and put them into the second, then there is the same in each. How many dollars does each contain ? Prove by trial with the result.
Suggestive Questions.—If one purse contains $6 and another $4, what is the difference between the purses ? What part of the difference must be taken from the one and put into the other to make them equal ? Then what must be the difference between two purses, when $30 taken from one and put into the other makes them equal ?
47. A says to B, give me $100, and I shall have as much as you. No, says B, give me rather $100, and then I shall have twice as much as you. How many dollars has each? Prove by trial with the result.
Suggestive Questions. What is the difference between B's money and A's ? (See the principle developed in the last exercise.) How much will that difference be increased if A gives B $100 ? How much will the whole difference then be ? If this difference makes B's money double that of A, how much, must A then have? How much, then, had A before he gave $100 to B? If A originally had and the difference was then —~, how much had B originally?
48. A copyist was asked how many sheets he wrote weekly, and answered, “I only work 4 hours a day, and cannot finish 70 sheets, which I wish to do; but if I could work 10 hours a day then I should write exactly as many above 70 sheets as I now write less than that number.” How many sheets did he write weekly ? Prove by trial.
Suggestive Question. If working 10 hours produces as great a surplus as working 4 hours does a deficiency, how many hours must he work to produce the exact result, or how many sheets would he finish in 4 and 10 hours ?
49. There are three brothers; the eldest 30, the 2d 20, and the 3d 6. When will the ages of the two younger amount to that of the elder? The sum of the ages of the two younger must, of course, increase with double the rapidity of the age of the elder. Prove by trial.
50. A baker works 313 days in a year (being the number of working days, except in leap-year and in those years which commence on a Sunday), and bakes 9 barrels of flour each day, at 196 lbs. a barrel. The bread weighs } more than the flour (on account of the water used). If he sell the bread at 4 cents a pound, how much will be his profit for the year, when the flour costs $5 per
Ans. $15,362.04. 51. A man who has $750 a year saves $145 annually. His income being raised to $1200, how much can he spend daily, counting 365 days to the year, if he save double as much as he did before ?
Ans. $24943. 52. I once had an untold sum of money lying before me. From this I took away the third part, and put in its stead $50. A short time after I took from the sum thus augmented, the 4th part, and again in its stead $70. I then counted the money, and found $120. What was the original sum ? Prove by trial.
Suggestive Questions.—What portion of the money is left when | is taken away? How much, then, after $50 is added ? How much is of +50 ? How much, then, remains after that is deducted ? How much, then, after $70 more is added ? Now, if į+$107-50 is equal to $120, how much is equal to ? Then how much is the whole ?
53. A cistern which is filled by two pipes in 12 minutes, can be filled by one of these pipes in 20 minutes ; in what time can it be filled by the other ?
Suggestive Questions.- What portion of the cistern is filled by both pipes in one minute? What portion is filled by one of them in one minute? The difference between those two fractions is equal to what ?
54. A cistern has two pipes. By one it can be filled in 20 minutes, and by the other in 30 minutes. What time will it require to fill it when both pipes are running ?
55. If 9 barrels of flour cost $45, what will 15 barrels cost ? See Practical Exercises on Fractional Quantities, p. 96, examples 5 to 16.
56. If 15 barrels of flour cost $75, what will 9 barrels cost ? 57. If a horse travel 30 miles in 6 hours, how many
miles will he travel in 11 hours ?
58. How many miles will a horse travel in 6 hours, if he can accomplish 55 miles in 11 hours ?
59. If 4 yards of cloth cost $12, what will 11 yards cost ?
60. What will be the price of 4 yards of cloth, when 11 yards cost $33 ?
61. If 3 men can mow a meadow in 10 days, in how many days can it be mowed by 6 men ?
62. When 6 men can mow a meadow in 5 days, how many days will be necessary for 3 to mow it? 63. If 3 qrs. of a yard of velvet cost 99 cts., how
many yards can I buy for $37.62 ?
64. If 281 yards of velvet cost $37662, what will be the cost of 3 quarters of a yard?
65. What is the value of a silver tankard, weighing 1 lb. 7 oz. 14 dwt., at 6s. 8d. per ounce ?
The pounds may be brought to ounces, and the pennyweights to the decimal of an ounce.
66. If a silver tankard, weighing 1 lb. 7 oz. 14 pwts., cost £6 11s. 4d., how much is that per ounce ?
67. If a staff, 4 feet long, cast a shade on level ground 7 feet long, what is the height of a steeple whose shade at the same time is 198 feet?
68. When a steeple, whose height is 198 feet, casts a shadow on level ground of the length of 346) feet, how long would be the shadow of a staff of 4 feet?
69. A journeyman pays $12 for 4 weeks' board. What will be his bill for 24 weeks at the same rate ? Ans. $72.
70. A farmer exchanged 30 bushels of rye for 120 bushels of potatoes. How much rye must he give at that rate for 600 bushels of potatoes ?
Ans. 150 bush. 71. If 10 men can build a wall, 360 rods long, in 9 days, how many rods can 1 man build in one day? 2 men in 1 day? 2 men in 2 days ? 24 men in 75 days ?
Ans, to last question, 7200. 72. If a man travel 100 miles in 5 days, travelling 4 hours each day, how far could he travel in 12 days, going 10 hours each day?
Ans. 600 miles. 73. If 6 men build a wall 20 feet long, 6 feet high, and 4 thick, in 16 days, in what time will 24 men build one 200 feet long, 8 feet high, and 6 feet thick? Ans. In 80 days.
74. If the freight of 8 hhds. of sugar, each weighing 121 cwt., 20 leagues, cost £16, what must be paid for the freight of 50 tierces, each weighing 21 cwt., 100 leagues ?
Ans. £100. 75. A journeyman paid $72 for 24 weeks' board; how much would be the charge for 4 weeks, at the same rate ?
Ans. $12. 76. How many yards of matting, 165 feet ide, will cover a room 18 feet wide, and 30 feet long ? Ans. 120 yards.
Suggestive Questions. How many square feet in the room? How many of these feet will be covered by 1 foot of matting ? How many feet of matting, then, will cover 540 square feet? How many yards, then ?