by this ratio, we have 155 fee: 852×28. Cancelling 6 of the numerator against 6, a factor of the 12 of the denominator, also cancelling 5, a factor of 155 of the numerator, against 5, a factor of 295 of the denominator, we get 31 feet 8599 2 6 6 2 2 5 6 1 9 7 feet, for the answer. 20. If 3 pounds of coffee cost 24 shillings, how much will 10 pounds cost?

26629

472

In this example, 24 shillings must be our third term; and since 10161 pounds must cost more than 34= pounds, we must divide 1 by for the ratio; making it 1x Multiplying the third term by this ratio, we obtain shillings xx; which, after cancelling, becomes of a shilling - shillings=73 shillings.

21. Gave $72 for 11 barrels of fish. How much will 88 barrels cost at the same rate? Ans. $576. 22. If 43 pounds of cheese cost $2-20, what will 216 pounds cost at the same rate? Ans. $11. 23. If I pay $3.90 for sawing 7 cords of wood, how much ought I to give for sawing 23 cords? Ans. $13. 24. If of a ship is worth $2853, what is the whole worth?

$2853

The ratio of the whole ship, or 18, to -35, is 0. Hence, $951×10=$9510 Ans. 25. If of my income is $533, what is my whole income? Ans. $1732.25.

26. A person failing in business, finds that he owes $7560, and that he only has $3100 to pay it with. How much can he pay to that creditor whose claim is $756? Ans. $310.

27. If it require 5 bushels of wheat to make one barrel of flour, how many bushels will it require for 100 barrels of flour? Ans. 550 bushels.

28. If 7 barrels of flour are sufficient for a family 6 months, how many barrels will they require for 11 months?

29. If it take 25 yards of carpeting, a certain floor, how many yards of necessary to cover the same floor?

Ans. 125 barrels. a yard wide, to cover carpeting would be Ans. 33 yards.

30. If a person travel 8 miles in 10 hours, how far will he travel in 5 days, by traveling 8 hours each day?

Ans. 32 miles.

31. If 35 pounds of feathers cost $15, what will 100 pounds cost at the same rate? Ans. $42.854. 32. If a man perform a certain piece of work in 18 days, when he works 8 hours per day, how many days will he require if he work 10 hours each day?

Ans. 14 days, 4 hours.

33. If a piece of board 12 inches wide and 12 inches long make one square foot, how many inches of length must be taken from a board 15 inches wide to make a square foot? Ans. 93 inches. 34. If 8 men can mow a field in 5 days, in how many days can 5 men do the same? Ans. 8 days. 35. If 27 yards of cloth cost $60, how many yards can I buy for $100? Ans. 45 yards. 36. If 27 yards of cloth cost $60, what will 455 yards cost? Ans. $100. 37. If of a ship is worth $9000, what is her whole value?

The whole ship being a unit, or, we have the ratio ; hence, the answer is $9000 x=$14400.

38. If of a city lot is sold for $500, what would of the same lot sell for at the same rate? Ans. $1166. 39. Admitting that the earth moves in its orbit about

56

Τ

the sun, a distance of 597000000 miles, in 365 days 6 hours, how far on an average does it move in each hour? Ans. 68104 miles. 40. The equatorial portions, by the diurnal rotation of the earth, moves about 24900 miles each day? How far is that in each hour? Ans. 1037 miles.

41. If it require 10 years of 3654 days for light to pass from a fixed star to the earth, how many miles distant is it, on the supposition that light moves 192000 miles in one second? Ans. 60590592000000 miles. 42. If by a leak of a ship enough water run in, in 4 hours, to sink her, how long can she survive?

Ans. 6hr. 40m.

how

43. If I pay $25 for the masonry of 4000 bricks, much ought I to pay for the work which requires 100000 bricks? Ans. $625.

44. If a steam-ship require 14 days to sail a distance of 3000 miles, what time, at the same rate of sailing, would she require to sail 24900 miles?

Ans. 116 days 44 hours. 45. Admitting the diameter of the earth to be 8000 miles, and the highest mountain to be 5 miles, what elevation must be made on the globe of 16 inches diameter to represent accurately the height of such mountain ? Ans. T of an inch. 46. If $100 in 12 months bring an interest of $7, how much will be the interest of $100 for 8 months?

Ans. $4.66.

47. If the interest of $100 for 12 months is $7, what will be the interest of $75 for the same time?

Ans. $5.25.

48. If in 12 months the interest of $100 is $7, how long must $100 be on interest to gain $10?

Ans. 174 months. 49. If a glacier of 60 miles in length move 50 inches per annum, in what time will it move its whole length? Ans. 76032 years.

50. If a staff of 10 feet in length give a shadow of 15 feet, how high is that tree whose shadow measures 90 feet? Ans. 60 feet.

51. Suppose sound to move 1100 feet in a second; how many miles distant is a cloud, in which lightning is observed 16 seconds before the thunder is heard, no allowance being made for the motion of light? Ans. 3 miles.

52. If it require 30 yards of carpeting which is of a yard wide to cover a floor, how many yards of carpeting which is 14 yards wide will be necessary to cover the same floor? Ans. 18 yards.

53. If the earth move through 12 signs, or 360° in 365 days, how far will she move in a lunar month of 29 days? Ans. 2937 degrees.

54. Suppose a steamboat capable of making 15 miles each hour, to move with a current whose velocity is 21 miles per hour, what will be the whole distance made during 13 hours? And what distance will the boat move in the same time against the same current ?

55. If the magnetic influence move through the telegraphic wires at the rate of 200000 miles in one second of time, how many times could it pass around the world in one second, allowing the circumference of the earth to be 24899 miles? Ans. 89 808 times.

2489

56. If A can do a piece of work in 7 days, and B can do it in 8 days, what part of it can both do in 3 days? Ans. 19 of it.

57. A reservcir, whose capacity is 1000 hogsheads, has a supply pipe by means of which it receives 300 gallons each hour; it also has two discharging pipes, the first of which discharges of a gallon each minute, the second discharges 1 gallons per minute. The reservoir being empty, in what time will it be filled if the supply pipe alone is opened? In what time, if the supply pipe and the first discharging pipe are opened? In what time, if the supply pipe and the second discharging pipe? And in what time, if all three are opened?

Supply pipe only opened, 210 hours 83 days.
(6
" and 1st dis. pipe, 252

=10

Ans.

46 "2d, 66

66 280 66

=11} .

COMPOUND PROPORTION.

110. When the quantity required depends upon more than three terms, the operation of finding it is called the Rule of Compound Proportion.

Suppose we have the following example:

If 6 men can mow 30 acres of grass in 5 days, by working 8 hours each day, how many acres can 4 men mow in 9 days of 10 hours each?

Had the number of days, as well as hours in each day, been the same in both cases, the question would have been equivalent to the following: