EXERCISE LVII.

1. Reduce 7 gals. 3 qts. 1 pt. to gallons and decimal of a gallon.

2. Reduce £4.375 to pounds, shillings, and pence. 3. Reduce 7.6875 gals. to gallons, quarts, and pints. 4. Reduce to pounds, shillings, and pence $5.875; $7.38; $17.85; $21.75; if $4.85 be equal to a pound.

5. How many square yards in 3.7156 acres?

6. If 2 qts. of linseed oil be 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 walk 88 mi. in 26 hrs. how many feet does he walk each second?

9. Of a mixture of sand and lime .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 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 rds. 2 yds. 2 ft. 6 in. to inches.

13. How many cubic inches in 2 cubic feet?

14. How many pounds avoirdupois does a cubic yard of water weigh if a cubic foot weigh 1000 ounces? 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 pks. of potatoes? 17. A farmer sowed 5 bu. 1 pk. 1 qt. of seed, and harvested

from it 103 bu. 3 pks. 5 qts. How much did he raise from a bushel of seed?

18. How many bushels in 5 t. of oats?

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

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

21. If a locomotive run at the rate of 111 rds. a minute, how many hours will it require to run from Boston to Buffalo, 498 miles?

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

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

24. What is the cost of 7 t. 1560 lbs. of hay at $15.50 a ton? 25. What is the cost of a car-load of wheat weighing 20,000 lbs. at $1.05 a bushel?

26. Reduce 5 rds. 4 yds. 24 ft. to the decimal of a mile. 27. Reduce 9 sq. ch. 11.25 sq. rds. to the decimal of an

acre.

28. Reduce .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 lbs. 6 oz. troy to the decimal of a ton avoirdupois.

34. Express 14.52 sq. yds. as the decimal of a square chain. 35. If a sovereign be equal to 25.22 francs, or to $4.85, what decimal of a dollar is a franc?

36. Express 2.805 florins-1.89 half-crowns as the decimal of £.472.

37. If .327 of some work be done in 3 hrs. 38 min., how long will the whole work require?

38. 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?

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

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

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

42. How long will it take to fill of a cistern, when the whole requires 6 hrs. 10 min.

43. The circumference of a circle is

is divided into 360 degrees.
55 degrees?

6 yds. 1 ft. 5.1 in., and

What is the length of

44. Multiply 2 t. 16 cwt. 634 lbs. by 14.

45. Into how many shares has £120 been divided when each share is £3 8s. 64d.?

46. If of one line be equal to & of another line, which is the greater? and what fraction of it is the less?

47. Multiply 5 mi. 206 rds. 2 ft. 2 in. by 786.

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

49. Divide 93 long tons 56 lbs. by 23 lbs. 5 oz.

50. Telegraph poles on railroads are generally erected at intervals of 88 yds. Show that if a passenger count 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.

51. If Greenwich time be 5 hrs. 8 min. 16 sec. later than

Washington time, and Chicago be 87° 35′ W., what

is the difference between Washington and Chicago time?

CHAPTER XIII.

PROBLEMS.

EXERCISE LVIII.

(1) A train travels 24 miles in 8 of an hour. Find its rate per hour.

If the question had been, a train travels 70 mi. in 2 hrs., its rate per hour would obviously be found by dividing the whole distance, 70 miles, by 2. The application of the same method to this question gives,

24 mi. + .8

=

30 mi. Ans.

(2) A train runs from New York to Philadelphia, 90 miles, in 1 hr. 33 min. What is its rate

per

hour?

583 mi. Ans.

1. A train from New York to Philadelphia, 90 miles, makes the whole distance in 2 hrs. 5 min. What is its rate? 2. Winlock, in 1869, found that electricity went through 7200 miles of wire in of a second. What was its

rate per second ? 3. If the time required for a signal to pass through the cable from Brest to Duxbury, 3799 miles, be .816 of a second, what is the rate per second?

4. If the report of a gun 14 miles distant is heard in 5g seconds after the flash is seen, what is the velocity of sound, in feet, per second?

5. If a man walk 33 miles in 46 minutes. what is his rate per hour?

6. If a horse go 47 miles in 10 hrs. 40 min., what is his average rate per hour?

7. If a stone on a glacier move 95 feet in 188 days, what is its rate, in inches, per day?

It is often required to express speed with reference to the unit of distance instead of the unit of time.

Ex. If a horse made 5 miles in 33 minutes, how long did it take him to make a mile?

33 min. ÷ 5 = 6 min. Ans.

Hence, when the time is required for the unit of distance, Divide the time by the distance.

8. If a horse trot of a mile in 2 minutes, in what time can he trot a mile?

9. If a train run 18 miles in 39 minutes, how long does it take to run one mile?

10. If sound travel 1125 feet a second, how long will it take to travel one mile?

11. If a train require 3 hours to travel 1044 miles, find its average time for travelling a mile.

12. If a mower cut 7 acres of grass in 3 days, what part of a day will it take him to cut one acre? If a day consist of 10 working-hours, what part of an acre does he cut in an hour?

13. If a mower cut 34 square rods in of an hour, how many acres can he cut in a day of 10 hours?

14. If a fountain yield 1174 gallons in of an hour, at what rate per hour is it flowing?

15. If a merchant's profits be $3147 in 74 months, what are his profits for a year?

16. If a wheel turn 17° 30′ in 35 minutes, in how many hours does it make a complete revolution?