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(6) If planes 0-1, 0-3, and 0-5 can each map a region alone in 10, 12, 15 hours, respectively, find how long it would take them to do the job together.

4 hr. Answer. 27. Miscellaneous exercises. (1) Solve for x:

4x—3=5x+9 (2) Evaluate when a=2, b=3, c=5: ab[a(a-c) -a3b2(6c)+a_b— b3c]

90 Answer. (3) Three observation airplanes, 0-4,0-7, and 0-9, wished to map a region. Each could do the work alone in 4, 6, and 8 hours, respectively. How long will it take all three airplanes to do the job together? (4) Solve for x:

8 1 +2

r=3 Answer.

3 (5) Solve for 3:

3 3

=0.

x+1 *+5 (6) One airplane can fly from San Diego to Victorville in 14 hours. Another airplane can make the trip in 2 hours. If they start from opposite ends of the course at the same time and fly toward each other, after what time will they meet?

% hr. Answer , (7) An airplane flying a course against the wind covers 160 miles in 1 hour. At a later time the airplane flies the return trip with the wind, with a ground speed of 200 miles per hour. If the round trip took 5 hours, what was the round-trip distance? (8) Solve for x:

Зr 4
(x—5)

=
x=13

Answer. 2 (9) Evaluate when x=-1, y=4, 2=2:

Xy.x2+4(yz+x) — 243 +y22 (10) One observation airplane can map a certain region in 1 hour. A second airplane can map the region in 14 hours. How long will it take the two to do it together.

35 hr. Answer. (11) A ferry pilot travels 800 miles by airplane and 100 miles by train in 4 hours 40 minutes. Then, at the same speeds as before, he flies 700 miles in another airplane and 150 miles by train in a total of 5 hours 20 minutes. What were the speeds of the airplanes and trains?

SECTION IV

29

SCALES

Paragraph Scope

28 Models Maps--

30 Miscellaneous exercises.

31 28. Scope.—The word "scale" is used in this section as in "scale model,” the "scale of a map," the "scale of a drawing," and so on. The practical use of scales in connection with maps, drawings, and silhouettes is illustrated by examples and exercises.

29. Models.—a. A true scale model of an airplane, for example, is a model which has been constructed so that the ratio of the length of any part of the model to the actual length of the same part of the airplane is the same for all parts. Thus, if the wing span on the model is 5 inches, and the wing span of the actual airplane is 55 feet, then 1 inch anywhere on the model represents 11 feet or 132 inches. Then this is the scale of the model: 1 to 132, or 7132. When a scale is stated simply as 1 to 132 it means that 1 unit of any kind on the model represents 132 of the same kind of units on the airplane. In other words, the model is 1132 the size of the airplane.

6. Example: The U. S. Government is encouraging youths to build scale models of various aircraft. The scale to be used is the same for all aircraft: 1 to 72. The wing span of the German Heinkel bomber (He-111K Mk111) is 76 feet. What will be the wing span of the model?

Solution: 76 feet=76X12 inches
wing span (model) 1
76 X 12 in. 72

76 X 12 76 Therefore, wing span of model=

= 123 in. Answer.

72 6 c. Exercises.The following models are all constructed to the scale of 1 to 72:

(1) The model wing span of a B-18 is 15 inches. What is the actual wing span?

(2) The over-all length of a Messerschmitt (Me-110) is 36 feet. How long will the model be?

6 in. Answer. (3) The over-all length of a model of a B-23 is 8% inches. What is the over-all length of the B-23 airplane?

30. Maps.-a. A map is a scale diagram to show the disposition of geographic features on the earth such as cities, roads, rivers, etc.

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On most maps, the scale used is conveniently stated by a diagram as in figure 23. It may also be expressed as a ratio, for example: 1 to 500,000.

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6. Of primary interest to airmen are aeronautical charts, or maps. The sectional charts of the United States are made to a scale of 1 to 500,000. The regional charts of the United States are made to a scale of 1 to 1,000,000.

Example: What distance (miles) does 1 inch represent on a sectional chart?

Solution: Since the scale is 1 to 500,000, then 1 inch represents 500,000 inches on the earth. 1 mile=5,280 feet=5,280 X 12 inches. Therefore

500,000 500,000 inches

miles=7.9 miles. 5,280 X 12

1 inch represents 7.9 miles. Answer. 31. Miscellaneous exercises. (1) On a regional chart 1 inch=how many miles?

(2) The aeronautical planning chart of the United States (3060a) is drawn to a scale of 1 to 5,000,000. On this chart, a distance of 2% inches is the same as how many

miles?

177.5 miles. Answer. (3) By direct measurement, determine the scale for the map in figure 24. From Catskill to Albany is 30 miles.

(4) How far is Schenectady from Albany? (See fig. 24.) Use the scale determined in exercise (3) above.

16 miles. Answer. (5) By direct measurement, determine the scale used for the map in figure 25. See exercise (3) above.

(6) Is Chatham located properly in figure 25? Why? (Its location is correct in figure 24.)

No. Answer. (7) The model of the German bomber Heinkel (He-177) has a wing span of 17% inches. What must be its actual wing span?

(8) The airplane models described in paragraph 296 will be used for training gunners in range determination. How far from the model should a gunner be so that it will appear to him as though the actual airplane were 600 yards away?

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Solution: His distance from the model should be in the same ratio to 600 yards as the model scale, or as 1 is to 72: distance 1

600 yd. or distance

Answer. 72 600 yd.

=8% yd.=25 ft.

72 (9) A top view silhouette of a B-23 is to be drawn as large as possible in a space 2 feet wide. The wing span of a B-23 is 91 feet. Which of the following scales should be used: 1 to 60, 1 to 100, 1 to 20, or 1 to 50?

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(10) Using the information in exercise (3) above, are the scales shown in figures 24 and 25 correct?

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