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. 633 lbs. by 14.

45. Into how many shares has £120 been divided when each share is £3 88. 64d.?

46. If 1 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?

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 5% 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?

de

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

If a stone on a glacier move 954 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 make 51 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 31 square rods in of an hour, how many acres can he cut in a day of 10 hours?

14. If a fountain yield 1171 gallons in & of an hour, at what rate per hour is it flowing?

15. If a merchant's profits be $3147 in 7 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?

17. If a man's expenditures be $4358 in 133 months, what is his yearly rate of expenditure?

18. If a cistern lose by leakage 7 gals. 1 pt. in 49 hrs. 40 min., what is its hourly rate of loss?

19. If the circumference of the earth at the equator be

24,900 miles, at what rate per hour is a person there

carried round, one whole rotation being made in 23 hrs. 56 min. ?

20. If a man travel 33 miles in 7 minutes, how many miles will he travel in 50 minutes? and how long will he take to travel 50 miles?

If a man can do a piece of work in 9 days, in 1 day he can do of the work.

If another man can do the same work in 8 days, in 1 day he can do of it; and

Both men together can do † + 1 = 1⁄2 of it in 1 day.

Therefore, if the whole work be considered to be divided into 72 equal parts, they can do 17 of these parts in 1 day, and the time required to do the whole work will be 72 ÷ 17 4 days.

=

Ex. A cistern can be filled by means of a water-pipe in 30 minutes, and can be emptied by a waste-pipe in 20 minutes. If the cistern be full, and both pipes be opened, in what time would it be emptied?

Therefore the whole will be emptied in 60 minutes.

21. If A can mow a certain meadow in 4 days, and B in 3 days, how long will it take both?

22. If A can lay a certain wall in 4 days, and B in 5 days, how long will it take both?

23. If a pipe will fill a vessel in 4

hours, and another in hours, how long will it take both to fill the vessel ?

3

24. If A can go from Boston to Albany in 94 hours, and B

from Albany to Boston in 11 hours, and they start

at the same time, in how many hours will they meet? 25. A requires 4 days, B 3 days, and C 4 days, to do a certain piece of work. How long will it take, all three working together?

26. A can mow of a field in 3 days; B can mow of it in 4 days. How long will it take both to mow the field? 27. One pipe can fill a cistern half full in & of an hour, and another can fill it three-quarters full in an hour. How long will it take both pipes to fill the cistern? 28. A cistern which holds 100 gallons can be filled from a pipe in 25 minutes, and emptied by a waste-pipe in 45 minutes. If both are opened together, how long will it take to fill the cistern, and how much water will be wasted?

29. A pipe can fill a cistern one-third full in of an hour; a waste-pipe can empty of the cistern in 20 minutes. If both pipes are opened, in what time will the cistern be filled?

30. If one pipe runs into a cistern at the rate of 2 gallons in 3 minutes, and another at the rate of 5 gallons in 4 minutes, while the water is running out of a third pipe at the rate of 4 gallons in 5 minutes, how long will it take to gain 71 gallons in the cistern?

31. A and B can do a piece of work in 21 days; A and C in 3 days; B and C in 44 days. Required the time in which all three, working together, can do the work, and in which each can do it alone.

Notice that by working two days each they can do the work.

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