1. A windmill pumps 2 gallons of water a minute; how many gallons does it pump in 1 hr.? In 10 hr. ?

2. When the wind blows 30 miles per hour a good windmill furnishes sufficient power to grind 25 bu. of grain per hour; at this rate, how many bushels would it grind in 10 hours? In 50 hours? In 100 hours?

3. A Wisconsin farmer found it possible to grind 50 bu. of corn per week for 7 months of the year; how many bushels did he grind? How many pounds did he grind in a week? (A bushel of corn weighs 56 lb.)

4. If the mill mentioned in Exercise 3 ran on the average 2 days per week, and the attendant received $1.40 per day, what was the cost per hundredweight of grain? What was the cost per pound?

5. It has been shown that when a gas-engine is used 4.822 bu. of corn are ground per hour for every horse power; how many pounds is this? Express the result to the nearest pound.

6. According to Exercise 5, how many bushels would a 5 horse-power engine grind in 10 hours? How many pounds?

7. When the gas required for the engine in grinding one hundredweight costs 1.3 cents, what will it cost for gas

enough to grind one ton?ton? ton? 1,500 lb.? 1,200 lb.?

ton?

800 lb.?

ton? ton? 1,800 lb. ?

8. If it takes 10 ft. of gas to grind 100 pounds of grain, what will it cost to grind a ton at $1.30 per 1,000 ft.?

9. A farmer can grind sufficient feed for a herd of 30 cows with a 12-foot windmill. Such a windmill and grinding equipment costs $225. If the grinding of his feed by others cost $50 per year, in how many years would the outfit pay for itself?

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ATMOSPHERIC PRESSURE

1. Although the atmosphere is relatively light it exerts a heavy pressure because of its great height above the earth's surface. Taking the average weight of air per cubic foot to be 1.2 oz. and the depth of the atmosphere as 51 mi., what is the weight of the column of air standing on 1 square foot? What is the atmospheric pressure, to the

nearest pound, on 1 sq. in. of surface?

2. According to Exercise 1, what is the atmospheric pressure on 5 sq. in.? On 10 sq. in.? On 15 sq. in.?

3. The picture shows a pipette or fountain-pen filler being filled with ink. When the fingers relax and allow the rubber part to expand, what forces the ink to rise up into the pipette?

4. If a hollow and perforated

rubber ball is squeezed and placed under water, why does it fill with water when released?

5. Press a piece of cardboard firmly over a glass filled with water. Invert the glass. If carefully done, the water will not spill when the hand is removed; why not?

6. If your book-cover is 8 in. long and 6 in. wide, what is the total pressure on its surface at 15 lb. per square inch? Why do you not have to lift this much in raising the book?

7. An incandescent light bulb has

a surface of about 20 sq. in. What is the air-pressure on this surface?

8. What is the pressure at 15 lb. per sq. in. on the total surface of a block 3 in. by 2 in. by 6 in. ?

PROBLEMS-REVIEW

79

1. How is the area of a triangle found? Illustrate your

7. How many board feet are there in a plank 12 in. wide, 12 ft. long, and 2 in. thick?

8. How many bunches of shingles of 250 each are there in 1,000 shingles?

66

9. In the measurement of a roof for tinning what is a square'? What is

the cost of tinning a roof 30 ft. by 40 ft. at $4 per square?

10. Find the area of a figure like the picture, and having the measurements as shown, by

2.33

6.5 in.

3.25 in.

4.5 in.

finding the area of each part separately and then adding.

II. In the ordinary cistern pump the air is drawn out of the pipe; what forces the water up the pipe?

12. If the cross-section of the pipe is 1 sq. in., what pressure does the air exert? The water will rise until it balances this pressure. In every inch of pipe there is a cubic inch of space. A cubic inch of water weighs oz., how high will it rise, if the pipe is long enough?

DECIMALS AND FRACTIONS

Oral and written.

Division

1. The area of a rectangle is 25.5 sq. in. and the altitude is 10 in.; what is the length of the base? How is the area of a rectangle found?

SUGGESTION.—Since 10 x base = 25.5, the base of 25.5.
How is of a number expressed decimally found?

2. The area of a rectangle is 3.5 sq. ft. and the base is 10 ft.; what is the altitude?

SUGGESTION.-Since 10 x altitude = 3.5, the altitude = of 3.5.
How is of a number expressed decimally found?

3. The area of a parallelogram is 327.5 sq. in. and the base is 100 in.; find the altitude. Use A for altitude.

SUGGESTION.-Since 100 × A = 327.5, A =

Too of 327.5.

How is of a number expressed decimally found?

4. The area of a rectangle is 3.6 sq. ft. and the altitude is .6 ft.; what is the length of the base? Use B for base.

SUGGESTION. -Since .6 x B = 3.6, B = 3.6 ÷

Why does 3.6 ÷ .6 = 36 ÷ 6 ?

6)36

5. The area of a parallelogram is 4.50 sq. yd. and the base is 2.25 yd.; what is the altitude?

SUGGESTION.-Since 2.25 × A = 4.50, A = 4.50 ÷

Why does 4.5 2.25 450 ÷ 225?

225)450

In dividing by a number containing a decimal it is convenient to multiply both divisor and dividend by 10, 100, . . ., so as to make the divisor a whole number. Why does this not alter the result?

Place the first figure of the quotient over the last figure of the dividend used to produce it.

PROBLEMS-DIVISION

I. The area of a parallelogram is 2.626 sq. yd. and the altitude is .26 yd.; find the base.

Why does 2.626.26 262.6 ÷ 26?

26)262.6

81

How is the position of the

decimal point in the quotient related to that of the decimal point in

8. 42.63.213.

9. 423.47.3. 10. 6.636.79. 11. 69.76.032. 12. 885.8÷1.11. 13. 97.336÷.47. 14. 121.67 2.3. 15. 80.48 1.64. 16. 160.05.05. 17. German silver is a mixture containing .55 by weight of copper, .25 of zinc, and .2 of nickel; how many ounces of copper are there in 100 ounces of German silver? How many ounces of zinc? Of nickel?

18. How many hundred ounces of German silver would contain 3.75 oz. of copper? How many ounces of zinc are there in the same amount of German silver? How many ounces of nickel?

19. At 2.4¢ per mile, the fare from New York to Chicago would be $21.60; find the distance.

20. At an average speed of 25.6 mi. per hour, how long will it take a train to go from Chicago to Denver (1,028 mi.)? 21. A rod contains 16.5 ft.; how many rods are there in a mile? In 2,541 ft.?

22. The pendulum of a clock made 120 swings in a minute; how long did it take the pendulum to make 1 swing?

23. If convenient, count the swings of some pendulum and find how long it takes it to make one swing.

24. A cubic inch of mercury weighs about .5 lb.; how many inches high must a tube whose base is 1 square inch be in order to hold 100 lb. of mercury?