64. A can do a and C in 6 days: together?

piece of work in 3 days, B in 4 days, in what time will they do it, working

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 40 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?

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, work.ng 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)?

6

10

}

:

STATEMENT.

12

9

}

:: 20 : X.

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.

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 re quired 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 buзnels 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 et thick, in 4 days; in what time will 48 men build a wall feet long, 6 feet high, and 3 feet wide?

7. If the freight of 80 tierces of sugar, each weighing 3 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 1 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 6 days of 12 hours

each, in how many days of 10 hours each will he travel 1293 miles?

17. If 120 men in 3 days, of 12 hours each, can dig a a trench of 30 yards long, 2 feet broad, and 4 feet deep, how many men would be required to dig a trench, 50 yards long, 6 feet deep, and 1 yards broad, in 9 days of 15 hours each?

18. If a stream of water running into a pond of 175 acres, raises it 10 inches in 15 hours, how much would a pond of 80 acres be raised by the same stream in 9 hours?

19. A person having a journey of 500 miles to perform, walks 200 miles in 8 days, walking 12 hours a day in how many days, walking 10 hours a day, will he complete the remainder of the journey?

20. If 1000 men, besieged in a town, with provisions for 28 days, at the rate of 18 ounces per day for each man, be reinforced by 600 men, how many ounces a day must each man have that the provisions may last them 42 days?

21. If a bar of iron 5 ft. long, 2 in. wide, and 13 in. thick, weigh 45 lb., how much will a bar of the same metal weigh that is 7 ft. long, 3 in. wide, and 24 in. thick?

22. If 5 compositors in 16 days, working 14 hours a day, can compose 20 sheets of 24 pages each, 50 lines in a page, and 40 letters in a line, in how many days, working 7 hours a day, can 10 compositors compose 40 sheets of 16 pages in a sheet, 60 lines in a page, and 50 letters in a line?

23. Fifty thousand bricks are to be removed a given distance in 10 days. Twelve horses can remove 18000 in 6 days: how many horses can remove the remainder in 4 days?

24. If 248 men, in 5 days of 11 hours each, dig a trench of 7 degrees of hardness, 2321 yards long, 33 wide, and 2 deep, in how many days, of 9 hours long, will 24 men dig a trench of 4 degrees of hardness, 337 deep?

yards long, 5 wide, and