7th, on what day, and at what time, did he reach Worksop? 8th, on what day, and at what time, did they meet on the road? 9th, at what distance from each place did the meeting take place? 25. To make 1 lb. of dough, 3 lb. of water and 3 lb. of flour are required. How much water and how much flour will it take to make 513 lbs. of bread, knowing that 14 lbs. of dough are reduced by baking to 1 lb. of bread? 26. If 1 oz. of silver make a wire 2352 yards long, how long will the wire be that is drawn out of 1 oz. of silver? 27. A thief, pursued by a constable, is 4 miles in advance. In what time will he be caught, if he goes 4 miles per hour, and the constable 1 mile in 8 minutes ? 28. What is the difference between of 1 bushel and of 1 peck? 29. A person having of a copper mine sells of his share for £572. 12s. How much is the whole mine worth? 30. Divide £1764. 18s. 6d. into 19 shares. 31. Express of a guinea-§ of £1 as a fraction of 10s. 6d. 32. Reduce of a yard to the fraction of 1 English ell? 33. 16 cwt. 3 qrs. 15 lbs. 8 oz. are what part of 1 ton? 34. In a farm, of the land is meadow, arable, and the remainder contains 64 ac. 3 ro. 28 pl. Find the quantities of meadow and arable land, and also the number of acres the farm contains. 35. A person owes each of 5 creditors £1. 10s.; to A he pays of his debt, to B, to C, to D, and to E. How much does he owe yet? 36. Express 24 days 15 hrs. 24 min. 16 sec. as the fraction of 365 days. 38. If I gain 24s. 6d. on £18. 18s., how much do I gain per £1? 39. What fraction of £12. 10s., together with £4 4s. 4d., will make £10. 10s. ? 40. A young lady's portion was £2400, which was of of her brother's fortune. How much was his fortune? ΤΣ 41. A bankrupt's assets are of his debts. How much will he pay in the £1 ? 42. If I had as much money as I have, half as much, and one-fourth as much more, I should have £198. How much have I ? 43. What part of 6d. is of £1. 1s. 14d.? 44. What is the difference between of of 1 guinea? of of a crown, and 45. A younger son received £133. 6s. 8d., which was of of his elder brother's portion, and 3 times the elder brother's was 1 times the father's property. How much was the father worth? 46. A party has a bill of £12. 7s. 1d. to pay, and one of them pays for himself and three friends £5. 9s. 10d. many were there? 47. The of £19. 16s. 9d. are of what? How 48. A man who was asked the time, answered, it is of of of of 24 hours. What time was it? 49. A person being asked the hour of the day, said that the time past noon was of the time till midnight. What was the hour? 50. A father left to his eldest son 4 of his property, to his second of the remainder, and to his third son what was left. What was the share of each, if the shares of the first and second differed by £1200? 51. A gets £4 of a legacy for B's £9, and C £5 for B's £12. A's share is £2000. What is the whole legacy? 52. If A, B, and C can build a wall in 24 days; B, C, and D in 27 days; C, D, and A in 32 days; and Ď, A, and B in 36 days, in what time would it be done by all of them together, and by each of them singly? 53. If 12 apples be worth as much as 21 pears, and 3 pears cost 1d., what is the price of 100 apples? 54. A cistern is filled by two pipes in 3 and 4 hours respectively, and a tap empties it in 1 hour. If these pipes be opened in order, at 1, 2, and 3 o'clock, prove that the cistern will be emptied at 12 minutes past five. 55. The consumption of coal in steam vessels is usually averaged at 7 lbs. per horse-power per hour. How many bushels of coal does an American steamer consume during her passage from Liverpool to New York, it being performed in 10 days 15 hours? The engines are two, of 250 horsepower each. About 82 lbs. of coal make 1 bushel. 56. A hare, pursued by a greyhound, is 50 leaps in advance; the greyhound takes 5 leaps whilst the hare takes 6, but 9 leaps of the hare make only 7 of the greyhound. How many leaps will the hare take before she is caught? 57. What number is that, of which exceeds of it by 144 ? 58. The pipe A fills a cistern in 5 hours, and B in 4 hours; C empties it in 2 hours. Suppose the cistern filled, and the three pipes left open, how much time will it take to empty it? 59. A poor woman bought some pears; for one-half she paid at the rate of a penny for 2, and for the other half a penny for 3. She sold them again at 5 for 2d., and was astonished to find she had lost 1d. by her bargain. How many had she? 60. Four persons divided £100 amongst themselves; the first received one-half of what the second got, which was two-thirds of what the third received, and the fourth had two-thirds as much as the other three. The amount of each person's share is required. PART VI. RULE OF 267. We have now arrived at the examination of questions which are usually solved by proportion; but since the properties of proportion depend more on algebraical than arithmetical principles, we propose postponing the demonstration of those principles, and to make use of a method which is superior, on account of its simplicity, conciseness, elegance, and rationality. It is from long experience in teaching that we prefer this plan to the ordinary one. Ex. 1. If 108 cwt. of sugar cost £448, what would 65 cwt. cost, at the same rate? .108 cwt. cost £448, .. 1 cwt. will cost of £448. or £43, or £17; Ex. 2. A pole, 8 feet long, casts a shadow of 7 feet. What is the height of a tower, which at the same time projects a shadow of 203 feet? ... 7 feet of shadow are cast by a pole of 8 feet, ... 1 foot Ex. 3. A person owes £3074. 6s. 8d., but can pay only £1921. 9s. 2d. What will be the dividend, shall I receive for a debt of £553. 3s.? £3074. 6s. 8d. are paid by £1921. 9s. 2d., ..£1 is paid by £1921.9s. 2d. £3074.6s. 8d. = and how much 3 x £3074. 6s. 8d. £5764. 7s. 6d. 9223 and..£553. 3s. are paid by 553 X 12s. 6d., or £345. 14s. 44d. 20 Ex. 4. If 12 men can do a work in 28 days, how many days will 20 men be doing the same? 12 men perform a work in 28 days, ..1 man performs the same in 12 × 28 days; and .20 men perform the same in of 12 × 28 days, or or 16 days. 12 × 28 20 5 Ex. 5. How much in length that is 7 feet 9 inches broad will be equivalent to what is 75 feet 6 inches long, and 7 feet 6 inches broad? .7 ft. 6 in., or 90 in. broad, require a length of 75 ft. 6 in. Ex. 6. The provisions in a garrison were sufficient to last 1800 men for 12 months; but at the end of 3 months the garrison was reinforced by 600 men, and two months after that a second reinforcement of 400 men was sent in. How long did the provisions last for the whole? 1800 men remain in the garrison 3 months, there is left 9 months' provisions for 1800 men, when the first reinforcement comes; then 1800 men have provisions for 9 months, .. 1 man has provisions for 1800 × 9 mo., or 16200 mo. ; but 1800+600, or 2400 men remain 2 months before the second reinforcement arrives, which is the same as 1 man remaining 2× 2400, or 4800 months, and the provisions would keep 1 man 16200 months; take away 4800 months and the difference expresses how many months' provisions would keep 1 man, when the second reinforcement was sent. .. 1 man has provisions for 16200-4800, or 11400 months; ..2400+400, or 2800 men will have provisions for of 11400 mo., or 4 months, and hence the provisions lasted 3+2+44 = 9 months. 268. Examples of this kind belong to that great variety of questions known under the name of Rule of Three, so called because three quantities being given, a fourth is found by means of them. In the three first examples, we may observe, that the answers increase and decrease respectively, as the quantities upon |