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29. A man can hoe a field of corn in 6 days, and a boy can hoe it in 9 days: how long will it take them both together to hoe it?

Analysis. Since the man can hoe the field in 6 days, in 1 day he can hoe of it; and since the boy can hoe it in 9 days, in 1 day he can hoe of it; consequently in 1 day they can both hoe + of the field. (Art. 202.) Now if of the field requires them both 1 day, s of it will require them of a day, and 4a will require them 18 times as long, or 18 of a day, which is equal to 33 days. Ans.

30. If A can chop a cord of wood in 4 hours, and B in 6 hours, how long will it take them both to chop a cord?

31. A can dig a cellar in 6 days, B in 9 days, and C in 12 days: how long will it take all of them together to dig it?

32. A man bought 25 pounds of tea at 6s. a pound, and paid for it in corn at 4s. a bushel: how many bushels did it take?

Analysis. If 1 lb. of tea costs 6s., 25 lbs. will cost 25 times as much, which is 150s. Again, if 4s. will buy 1 bushel of corn, 150s. will buy as many bushels as 4s. is contained times in 150s.; and 150s.÷4=37 times. Ans. 37 bushels.

463. The last and similar examples are frequently arranged under the rule of Barter.

Barter signifies an exchange of articles of commerce at prices agreed upon by the parties.

OBS. Such examples are so easily solved by Analysis that a specific rule for them is unnecessary.

33. A farmer bought 110 lbs. of sugar at 18 cents a pound, and paid for it in lard at 5 cents a pound: how much lard did it take?

34. How much butter, at 12 cents a pound, must be given for 250 lbs. of tea, at 75 cents a pound?

35. How many cords of wood, at $2 per cord, must be given for 56 yds. of cloth, at $44 per yard?

36. How many pair of boots, at $4.50 a pair, must be given for 50 tons of coal at $9 per ton?

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37. A, B, and C, united in business; A put in $250; and C, $340; they gained $258: what was each man's the gain?

Analysis.-The whole sum invested is $250 +$270+ $860. Now since $860 gain $258, it is plain $1 will gain $258, which is 30 cents. And

If $1 gains 30 cts. $250 will gain $250X.30=$75, A'

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Or, we may reason thus: Since the sum invested is $86 A's part of the investment is equal to 250, or 25;

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A must receive 25 of the whole gain $258=$75;

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464. When two or more individuals associate themselve gether for the purpose of carrying on a joint business, the u is called a partnership or copartnership.

OBS. The process by which examples like the last one are solved, is called Fellowship.

38. A and B join in a speculation; A advances $1500 and $2500; they gain $1200: what was each one's share of the ga

39. A, B, and C, entered into partnership; A furnished $300 B $4000, and C $5000; they lost $1800: what was each on share of the loss?

40. A's stock is $4200; B's $3600; and C's $5400; the who gain is $2400 what is the gain of each?

41. A's stock is $7560; B's $8240; C's $9300; and D $6200; the whole gain is $625: what is the share of each?

42. A bankrupt owes one of his creditors $400; another $500 and a third $600; his property amounts to $1000: how much can he pay on a dollar; and how much will each of his creditors receive?

OBS. The solution of this example is the same in principle as that of Ex. 37.

465. Examples like the preceding are commonly arra under the rule of Bankruptcy.

Notc,-A bankrupt is a person who is insolvent, or unable to pay his debts.

43. A bankrupt owes $5000, and his property is worth $35 how much can he pay on a dollar?

44. A man died owing $16400, and his effects were sold $4100 what per cent. did his estate pay?

45. If a man owes A $6240, B $8760, and C $9000, and but $11500, how much will each creditor receive?

46. If I owe $48000, and have property to the amount $32000, what per cent. can I pay?

47. What per cent. can a man pay, whose liabilities $120000, and whose assets are $45000?

48. What per cent. can a man pay, whose liabilities $1500000, and whose assets are $150000?

466. It often happens in storms and other casualties at that masters of vessels are obliged to throw portions of t cargo overboard, or sacrifice the ship and their crew. In s cases, the law requires that the loss shall be divided among owners of the vessel and cargo, in proportion to the amoun each one's property at stake.

The process of finding each man's loss, in such instance called General Average.

OBS. The operation is the same as that in solving questions in bankru and partnership.

49. A, B and C, freighted a ship from New York to Liverp A had on board 100 tons of iron, B 200 tons, and C 300 t in storm 240 tons were thrown overboard: what was the of each?

50. A packet worth $36000 was loaded with a cargo value $65000. In a tempest the master threw overboard $25250 w of goods what per cent. was the general average?

51. A steam ship being in distress, the master threw the cargo overboard; finding she still labored, he afterwa threw overboard of what remained. The steamer was w

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$120000, and the cargo $240000: what per cent. was t average, and what would be a man's loss who owned c and cargo?

52. A man mixed 25 bushels of peas worth 6s. a bu 15 bushels of corn worth 4s. a bushel, and 20 bushel worth 3s. a bushel: what was the mixture worth per bu Analysis.-25 bu. peas at 6s.=150s., value of the pea

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and 270s., value of whole m Now if 60 bu. mixture are worth 270s., 1 bu. mixture i of 270s.; and 270s.÷60=44s. Ans.

PROOF.-60 bu. at 44s.=270s., the value of the whole m

467. The process of finding the value of a compound tare of articles of different values, or of forming a com which shall have a given value, is called Alligation. Alliga usually divided into two kinds, Medial and Alternate.

OBS. 1. When the prices of the several articles and the number or q of each are given, the process of finding the value of the mixture, as in t example, is called Alligation Medial.

2. When the price of the mixture is given, together with the price of article, the process of finding how much of the several articles must be to form the required mixture, is called Alligation Alternate Alligation nate embraces three varieties of examples, which are pointed out in the fo ing notes.

53. If you mix 40 gallons of sperm oil worth 8s. per ga with 60 gallons of whale oil worth 3s. per gallon, what will mixture be worth per gallon?

54. At what price per pound can a grocer afford to sell a m ture of 30 lbs. of tea worth 4s. a pound, and 40 lbs. worth 7 pound?

55. If 120 lbs. of butter at 10 cts. a pound are mixed with lbs. at 8 cts. and 24 lbs. at 5 cts. a pound, what is the mixtu worth?

56. A tobacconist had three kinds of tobacco, worth 15, 1 and 25 cents a pound: what is a mixture of 100 lbs. of eac worth per pound?

57. A liquor dealer mixed 200 gallons of alcohol worth 50 cts. a gallon, with 100 gallons of brandy worth $1.75 a gallon: what was the value of the mixture per gallon?

58. A grocer sells imperial tea at 10s. a pound, and hyson at 4s.: what part of each must he take to form a mixture which he can afford to sell at 6s. a pound?

Note 1.-It will be observed in this example that the price of the mixture and also the price of the several articles or ingredients are given, to find what part of each the mixture must con ain.

Analysis. Since the imperial is worth 10s. and the required mixture 6s., it is plain he would lose 4s. on every pound of imperial which he puts in. And since the hyson is worth 4s .a pound and the mixture 6s., he would gain 2s. on every pound of hyson he puts in. The question then is this: How much hyson must he put in to make up for the loss on 1 lb. of imperial? If 2s. profit require 1 lb. of hyson, 4s. profit will require twice as much, or 2 lbs. He must therefore put in 2 lbs. of hyson to 1 lb. of im

perial.

PROOF-2 lbs. of hyson, at 4s. a pound, are worth 8s., and 1 lb. of imperial is worth 10s. Now 8s.+10s.=18s. And if 3 lbs. mixture are worth 18s., 1 lb. is worth of 18s., which is 6s., the price of the mixture required.

59. A farmer has oats which are worth 20 cts. a bushel, rye 55 cts., and barley 60 cts., of which he wishes to make a mixture worth 50 cts. per bushel: what part of each must the mixture contain?

Analysis. The prices of the rye and barley must each be compared with the price of the oats. If 1 bu. oats gains 30 cts. in the mixture, it will take as many bu. of rye to balance it, as 5 cts. (the loss per bu.) are contained times in 30 cts., viz: 6 bu. Again, since 1 bu. oats gains 30 cts., it will take as many bushels of barley to balance it, as 10 cts. (the loss per bu.) are contained times in 30 cts., viz: 3 bu. Hence, the mixture must contain 2 parts of oats, 6 parts rye, and 3 parts barley.

60. If a man have four kinds of sugar worth, 8, 9, 11, and 12

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