1. Reduce 7 gal. 3 qt. 1 pt. to gallons and the decimal of a gallon.

2. Reduce £4.375 to pounds, shillings, and pence.

3. Reduce 7.6875 gal. to gallons, quarts, and pints.

4. If $4.85 is equal to a pound, reduce to pounds, shillings, and pence $5.875; $7.38; $17.85; $21.75.

5. How many square yards in 3.7156 A.?

6. If 2 qt. of linseed oil are mixed with pt. spirits of turpentine, what fraction of the mixture is turpentine? How much turpentine in one pint of the mixture?

7. Reduce 5.1732 mi. to yards, feet, and inches.

8. If a man walks 88 mi. in 26 hr., how many feet does he walk in a second?

9. Of a mixture of sand and lime 0.27 of the weight is lime. How many ounces of lime in a pound of the mixture? How many troy grains of lime in an avoirdupois pound of the mixture?

10. A gill of water is put into a quart measure, and the measure then filled with milk. What part of the mixture is water?

11. Reduce 555 ft. to the decimal of a mile.

12. Reduce 1 mi. 13 rd. 2 yd. 2 ft. 6 in. to inches.

13. How many cubic inches in 2 cu. ft. ?

14. How many pounds avoirdupois does a cubic yard of water weigh if a cubic foot weighs 1000 oz. ?

15. Express the weight of a cubic yard of water as the decimal of a ton.

16. What is the weight of 7 bu. 3

17. A farmer sowed 5 bu. 1 pk. 1 vested from it 103 bu. 3 pk. 5 qt. raise from a bushel of seed?

pk. of potatoes? qt. of seed, and har

How much did he

18. How many bushels in 5 tons of oats?

19. How many bottles, each holding 1 pt. 3 gi., can be filled from a barrel of cider ?

20. If a steamer makes 13 mi. 6 rd. an hour, how far will she go between 6 A.M. and 6 P.M.? How many hours will she require to make 113 mi. ?

21. If a train runs at the average rate of 111 rd. a minute, how many hours will it require to run from Boston to Buffalo, 498 mi. ?

22. What is the cost of 12 A. 146 sq. rd. of land at $16.25 an acre?

23. What is the cost of 8 t. 3 cwt. 27 lb. of coal at $5.75 a ton?

24. What is the cost of 7 t. 1560 lb. of hay at $15.50 a ton?

25. What is the cost of a car load of wheat weighing 20,000 lb. at $1.05 a bushel ?

26. Reduce 5 rd. 4 yd. 2 ft. to the decimal of a mile.

27. Reduce 9 sq. ch. 11.25 sq. rd. to the decimal of an

acre.

28. Reduce 0.09375 bu. to quarts.

29. Reduce 7560 chains to miles.

30. How many gross are 2000 pens ?

31. Find the cost of 27.248 A. at $93.75 an acre.

32. Which is the greater, 2.8 of 3 ft. 11 in. or 3.11 of 2 ft. 8 in., and by how much?

33. Reduce 171 lb. 6 oz. troy to the decimal of a ton avoirdupois.

34. Express 14.52 sq. yd. as the decimal of a square chain.

35. If a sovereign is equal to 25.22 francs, or to $4.85, what decimal of a dollar is a franc?

36. If 0.327 of some work is done in 3 hr. 38 min., how long will the whole work require ?

37. A can run a mile in 7.68 min.; B can run at the rate of 7.68 mi. an hour. Which is the faster runner?

38. How many miles an hour does a person walk who takes 2 steps a second and 1900 steps in a mile?

39. If an ounce troy of gold is worth $20, what is the value of a pound avoirdupois?

40. Two stars cross the meridian at 6 hr. 4 min. 42.3 sec. and 7 hr. 2 min. 57.21 sec., respectively. What is the interval between the observations?

41. How long will it take to fill of a cistern, when the whole requires 6 hr. 10 min.?

42. The circumference of a circle is 6 yd. 1 ft. 5.1 in. What is the length of an arc of 55° ?

43. Multiply 2 t. 16 cwt. 633 lb. by 13.

44. Into how many shares has £120 been divided when each share is £3 8s. 6 d.?

45. If of one line is equal to 8 of another line, which is the greater? What fraction of the greater is the less? 46. Multiply 5 mi. 206 rd. 2 ft. 2 in. by 786.

47. The returns of a gold mine are 241 t. of ore yielding 2 oz. 1 dwt. 15 gr. of fine gold a ton, and 193 t. yielding 1 oz. 12 dwt. 9 gr. a ton. Find the value of the whole yield, at $19.45 an ounce.

48. Divide 93 long tons 56 lb. by 23 lb. 5 oz.

49. Telegraph poles on railroads are generally erected at intervals of 88 yd. Show that if a passenger counts the number of poles which the train passes in three minutes, that number will express the number of miles an hour the train is going.

50. If Greenwich time is 5 hr. 8 min. 16 sec. later than Washington time, and Chicago is 87° 35' W., what is the difference between Washington time and Chicago time?

51. What fraction of 21 cu. yd. 11 cu. ft. 1215 cu. in. is 3 cu. yd. 1 cu. ft. 1161 cu. in.?

52. How many minutes in the first three months of 1895 ? How many in the first three months of 1896 ?

53. A knot is of a degree, and a mile is 0.01477 of a degree. Find in miles the value of a knot to five decimals. 54. The captain of a steamer, sailing from Liverpool, found on taking an observation that the sun crossed his meridian at 42 min. 5 sec. past one o'clock P.M. by Greenwich time. Find his longitude.

55. If a walk 6 ft. wide is made round a park 600 ft. square within the enclosure, how many square yards will the walk contain?

56. How many pickets 3 in. wide, placed 3 in. apart, will be required to fence a rectangular lot 231 ft. long and 99 ft. wide? What will they cost at $3.25 per hundred?

57. The length of a year is 365.242218 mean solar days. Express the length of a year in days, hours, minutes, and

seconds.

58. The Flying Dutchman Express runs from London to Exeter, a distance of 1934 mi., in 44 hr., making one stop of 10 min., two of 5 min. each, and one of 3 min. What is its average speed per hour when in motion?

59. The Scotch Express runs from London to Edinburgh, a distance of 3933 mi., in 9 hr., making one stop of 30 min., three of 5 min. each, and one of 3 min. What is its average speed per hour when in motion?

60. The Empire State Express runs from New York to Buffalo, a distance of 439 mi., in 8 hr. 15 min., making two stops of 3 min. each and two stops of 2 min. each. is its average speed per hour when in motion?

What

61. How many dollars worth 4s. 2d. each will pay a bill of £11 17s. 6d.?

62. The lunar month is 29.53059 days. Express the length of a lunar month in days, hours, minutes, and seconds.

CHAPTER IX.

PROBLEMS.

342. Arithmetical Analysis. If the value of any number of units is given, we may by division find the value of one unit of the same kind, and by multiplication the value of any number of units of the same kind. The solution which combines these two processes is called analysis.

Example. If 18 yards of cloth cost $45, what will be the cost of 27 yards of cloth ?

SOLUTION. If 18 yd. of cloth cost $45, 1 yd. will cost of $45, or $24. If 1 yd. of cloth costs $24, 27 yd. will cost 27 × $21, or $674.

EXERCISE 87.

1. If 15 yards of silk cost $18.75, what will be the cost of 20 yards?

2. If 3 pounds of tea cost $3.80, how many pounds can be bought for $21.89 ?

3. If3 of a ton of coal costs $1.12, what is the price of 5 cwt.?

4. If of a piece of work is done in 25 days, what fraction of the work will be done in 113 days?

5. A bankrupt's debts are $2520, and the value of his property is $1890. How much can he pay on a dollar?

6. If a bankrupt's debts are $4264, and he pays 621 cents on a dollar, what are his assets ?