for the same time, when the army is increased to 4500 men?

53. A grocer bought a hogshead of rum for 80 cents a gallon, and after adding water sold it for 60 cents a gallon, when he found that the selling and buying prices were proportional to the original quantity and the mixture: how much water did he add?

54. A man failing in business, pays 60 cents for every dollar which he owes; he owes A $3570, and B $1875: how much does he pay to each?

55. A bankrupt's effects amount to $2328.75, his debts amount to $3726: what will his creditors receive on a dollar?

56. If a person drinks 80 bottles of wine in 3 months of 30 days each, how much does he drink in a week?

57. If 4 yards of cloth cost 14s. 8d. New York currency, what will 40 yards cost?

58. If a grocer uses a false balance, giving only 142 oz. for a pound, how much will 1547 lb. of just weight give, when weighed by the false balance?

59. If a dealer in liquors uses a gallon measure which is too small by of a pint, what will be the true measure of 100 of the false gallons?

60. After A has travelled 96 miles on a journey, B sets out to overtake him, and travels 23 miles as often as A travels 19 miles: how far will B travel before he overtakes A ?

61. A person owning of a coal mine, sold of his share for $9345: what was the value of the whole mine? ox 62. At what time, between 6 and 7 o'clock, will the hour and minute hands of a clock be exactly together?

63. If a staff, 5 feet long, casts a shadow of 7 feet, what is the height of a steeple, whose shadow is 196 feet, at the same time of day?

64. A can do a piece of work in 3 days, B in 4 days, and C in 6 days in what time will they do it, working together?

:

65. A can build a wall in 15 days, but with the assistance of C, he can do it in 9 days: in what time can C do it alone?

66. If 120 men can build mile of wall in 15 days, how many men would it require to build the same wall in 403 days?

67. If 3 horses, or 5 colts, eat a certain quantity of oats in 40 days, in what time will 7 horses and 3 colts consume the same quantity?

68. If a person can perform a journey in 24 days of 101 hours each, in what time can he perform the same journey, when the days are 12 hours long?

69. A piece of land, 40 rods long and 4 rods wide, is equivalent to an acre: what is the breadth of a piece 15 rods long that is equivalent to an acre?

70. If a person travelling 12 hours a day finishes one-half of a journey in ten days, in what time will he finish the remaining half, travelling 9 hours a day?

71. How many pounds weight can be carried 20 miles, for the same money that 4 cwt. can be carried 36 miles?

72. If 72 horses eat a certain quantity of hay in 7 weeks, how many horses will consume the same in 90 weeks?

73. A watch, which is 10 minutes too fast at 12 o'clock, on Monday, gains 3 min. 10 sec. per day: what will be the time, by the watch, at a quarter-past ten in the morning of the following Saturday?

53618

74. Two persons, A and B, are on the opposite sides of a wood, which is 536 yards in circumference; they begin to travel in the same direction at the same moment; A goes at the rate of 11 yards per minute, and B at the rate of 34 yards in 3 minutes: how many times must A go round the wood before he is overtaken by B?

DOUBLE RULE OF THREE.

244. THE DOUBLE RULE OF THREE is an application of the principles of Compound Proportion.

1. If 8 men in 12 days can build 80 rods of wall, how much will 6 men build in 18 days?

2. If 20 men can perform a piece of work in 12 days, working 9 hours a day (that is, in 108 hours), how many men will accomplish the same work in 6 days, working 10 hours a day (that is, in 60 hours)?

STATEMENT.

61 10

:: 20 :

Ꮖ .

OPERATION.

12 × 9 × 20

ANALYSIS.-Write the required term, x, in the 4th place, and 20 men, having the same unit, in the 3d place. Since 20 men require 108 hours to do the work, more men will be required to do the same work in 60 hours; therefore, the terms named in connection with each other, are inversely proportional: hence, 6 x 10 = 60, must be written in the first place.

X=

6 × 10

= 36 men.

3. If 24 men, in 6 days, working 7 hours a day, can build a wall 115 feet long, 3 feet thick, and 4 feet high, how long a wall can 36 men build in 12 days, working 14 hours a day, if the wall is 4 feet thick and 5 feet high.

244. What is the double rule of three?

I. Write the required term, or the term containing the required element, in the 4th place, and the term having the same unit value in the third place:

II. Then analyze the question, and see whether the terms named in connection with each other are directly or inversely proportional: when directly proportional, write the term named in connection with the 4th term, in the 2d place; and when inversely, write it in the first place: then find the required term or element (Art. 242).

Examples.

1. If 2 men can dig 125 rods of ditch in 75 days, in how many days can 18 men dig 243 rods?

2. If 400 soldiers consume 5 barrels of flour in 12 days, how many soldiers will consume 15 barrels in 2 days?

3. If a person can travel 120 miles in 12 days of 8 hours each, how far will he travel in 15 days of 10 hours each?

4. If a pasture of 16 acres will feed 6 horses for 4 months. how many acres will feed 12 horses for 9 months?

5. If 60 bushels of oats will feed 24 horses 40 days, how long will 30 bushels feed 48 horses?

6. If 82 men build a wall 36 feet long, 8 feet high, and 4 feet thick, in 4 days; in what time will 48 men build a wall 864 feet long, 6 feet high, and 3 feet wide?

7. If the freight of 80 tierces of sugar, each weighing 31 hundredweight, for 150 miles, is $84, what must be paid for the freight of 30 hogsheads of sugar, each weighing 12 hundredweight, for 50 miles?

8. A family consisting of 6 persons, usually drink 15.6 galons of beer in a week: how much will they drink in 12.5 weeks, if the number be increased to 9?

9. If 12 tailors in 7 days can finish 14 suits of clothes. how many tailors in 19 days can finish the clothes of a regiment of 494 men?

10. If a garrison of 3600 men eat a certain quantity of bread in 35 days, at 24 ounces per day to each man, how many men, at the rate of 14 ounces per day, will eat twice as much in 45 days?

11. A company of 100 men drank £20 worth of wine at 2s. 6d. per bottle: how many men, at the same rate, will £7. worth supply, when wine is worth 1s. 9d. per bottle?

12. A garrison of 3600 men has just bread enough to allow 24 oz. a day to each man for 34 days; but a siege coming on, the garrison was reinforced to the number of 4800 men: how many ounces of bread a day must each man be allowed, to hold out 45 days against the enemy?

13. Bought 5000 planks, 15 feet long and 2 how many planks are they equivalent to, of 12 14 inches thick?

inches thick ; feet long and

14. If 12 pieces of cannon, eighteen-pounders, can batter down a castle in 3 hours, in what time would nine twenty-fourpounders batter down the same castle, both pieces of cannon being fired the same number of times, and their balls flying with the same velocity?

15. If the wages of 13 men for 7 days, be $149.76, what will be the wages of 20 men for 15 days?

16. If a footman travel 264 miles in 63 days of 12 hours