20. A farm containing 46 A. 134 P. rents for $374.70 per annum, what will be the rent on 35 A. 90 P. at the same rate?

21. If 12 men can do a piece of work in 5 days, in how many days can 8 men and 5 boys do the work, if a man can work 21 times as fast as a boy?

22. A prisoner escaped from jail and traveled at the rate of 6 miles an hour. In 5 hours the constable started in pursuit, traveling at the rate of 9 miles an hour. In how many hours after breaking jail was the prisoner overtaken?

5

23. A and B can perform a piece of work in 5 days. A and C can do the same work in 6 days. B and C can do it in 63 days; in what time can each do the work alone, and how long will it take all of them together to do it?

COMPOUND PROPORTION.

284. A compound proportion involves two or more simple proportions; and any problem in compound proportion may be solved as a question in simple proportion, by making several successive statements.

ILLUSTRATION.

1. If 4 men earn $20 in 5 days, how much can 7 men earn in 12 days?

Solution.

As the answer is to be dollars, the third term must be 20. Since 4 men earn $20, 7 men can earn more. Hence, 4:7::20:35. Again: Since $35 are earned in 5 days, more can be earned in 12 days; hence, 5:12::35:84. Hence, 7 men in 12 days earn $84.

STATEMENT IN COMPOUND PROPORTION.

ARRANGEMENT OF CONDITIONS.

1st. Condition: 4 men, $20, 5 days.

2d. Condition: 7 men,

12 days'

Statement. As the answer is to be dollars the third term must be 20. Since 4 men earn $20, 7 men earn more. Then, the first couplet reads 4: 7. Since $20 are earned in 5 days, in 12 days more can be earned. Then, the second couplet reads 5: 12. Then,

4:71

5:12

:: 20: the missing term. Solving this, we get

7X 12 X 20
4 X 5

-84.

2. If 20 men, by working 3 hours a day, can do a piece of work in 15 days, how many men will be required to do the same work in 12 days, working 5 hours a day?

ARRANGEMENT OF CONDITIONS.

1st. Condition: 20 men, 3 hours, 15 days.

2d. Condition: men, 5 hours, 12 days.

1st. What is the third term? Why?

2d. Will it require more, or less, men to do the work in 12 days than it will to do it in 15 days? Why?

3d. Will it require more, or less, men to do the work when they work 5 hours a day, than it will when they work 3 hours a day? Why?

STATEMENT IN COMPOUND PROPORTION.

RULE.-I. Arrange the terms in the second condition under the corresponding terms in the first condition.

II. Select the third term as in simple proportion.

III. Arrange the terms in each couplet (without reference to any of the other couplets) as in simple proportion.

IV. Multiply the third term by the continued product of the second terms of the several couplets, and divide this product by the continued product of the first terms of the several couplets.

NOTE. If any couplet contains different denominations, reduce both terms to the lowest denomination in either term of the couplet.

MISCELLANEOUS EXAMPLES.

1. How many men will be required to do a piece of work in 25 days, working 7 hours each day, if 30 men can do it in 14 days, working 15 hours each day?

2. Four men by working 10 hours a day for 12 days can dig a ditch 24 yards long, 9 feet wide, 5 feet deep; how many hours a day must 3 men work to dig a similar ditch 10 yards long, 12 feet wide, 6 feet deep, in 10 days?

3. A loaned B $1500 for 9 months when money was worth 7 per cent. ; for what time must B loan A $1800 when money is worth 31 per cent. per annum?

4. What sum of money loaned at 6 per cent. for 10 months will yield the same income as $750 loaned for 12 months at 4 per cent.? Ans. $600.

5. It requires 200 men to build a stone wall 100 rods. long, 4 feet high, 31⁄2 thick, in 2 days, working 6 hours a day. How many men will be required to build a

wall 75 rods long, 5 feet high, 7 feet thick, if the work is 23 times as difficult?

6. If 5 oxen or 7 cows eat the grass on 3 acres in 87 days, in what time will 3 cows and 2 oxen eat the grass on 10 acres.

7. A man bought city lots at $40 per front foot, which were supposed to measure 961 feet. There was an error of of an inch in the 12 foot pole used in measuring it. How much was he cheated?

8. A marble slab 15 feet long, 2 feet wide, 4 inches thick, weighs 2000 lbs. ; what is the thickness of a similar slab 25 feet long, 5 feet wide, weighing 3500 lbs?

9. It requires of a bushel of oats to keep 4 horses of a day, how many horses will 9 bushels feed & of a day? Ans. 160.

10. If 20 acres in St. Louis are worth 30 acres in Cincinnati, 50 acres in Cincinnati are worth 45 acres in Chicago, 25 acres in Chicago are worth 20 acres in Boston, and 33 acres in Boston are worth 40 acres in New Orleans, how many acres in St. Louis are equal in value to 1800 acres in New Orleans?

11. Forty men agree to do a piece of work in 50 days, but after working 9 hours per day for 30 days, they find they have completed but the work. How many extra men must they employ to finish the work according to agreement by working 10 hours per day?

12. Fifteen men eat 13 shillings' worth of bread in 6 days, when wheat is sold at 12 shillings per bushel; in what time will 30 men eat 431 shillings' worth, when wheat is selling at 10 shillings per bushel?

13. If 10 yards are required to make a suit of clothes, how many yards must a man buy when the cloth is 17 yards wide, so as to allow for shrinkage 5 per cent. in length, and the same in width?

14. If the type for a book of 84 pages, 50 lines on a page, lines averaging 8 words, 1 syllables to a word, 21 letters to a syllable, was set by two men in five days of 12 hours each, how many pages of a book, each page containing 75 lines, averaging 5 words each, 2 syllables to a word, 3 letters to a syllable, would be set by 7 men, laboring 8 hours a day for the working days of a week?

15. If 12 men, in two months of 4 weeks each, working 6 days per week, 12 hours a day, can set the type for 12 books of 600 pages, 120 lines to a page, 20 words to a line, 10 letters to a word, in how many months of 4 weeks each, will 7 boys, working 4 days per week, 16 hours a day, set the type for 6 books, of 500 pages each, 150 lines to the page, lines averaging 24 words, 4 letters to a word, each boy doing of the work of a man?

285. GENERAL REVIEW.

1. Define ratio.

2. Simple ratio.

I. RATIO.

3. Compound ratio.

4. Antecedent; consequent.

a. Which is dividend?

b. Which is divisor?