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12-13 ARMY AIR FORCES

(9) A mechanic and assemble 10/32 of a motor in 1 day. How many motors can he assemble in 3 3/5 days?
(10) If a pilot flies 347 miles in 3 hours, 15 minutes, how far will he travel at the same rate in 7 hours, 45 minutes?
827.46 miles. Answer.

13. Ratio and proportion.-a. Consider two bombs, one weighing 300 pounds and the other 100 pounds. The first is three times as heavy as the second, or the second is one-third as heavy as the first. This may be expressed as "the ratio of the weight of the second bomb to the weight of the first bomb is 1/3." In other words, a ratio is the quotient of two like quantities. In this example,

ratio=100 lb/300 lb = 1/3

b. The statement that two ratios are equal is called a proportion. Thus, for example, if the explosive in the first bomb is 270 pounds, and the explosive in the second bomb is 90 pounds, then the ratios of the explosives are also 1/3, and

100 lb/300 lb = 90 lb/ 270 lb

is called a proportion.

c. The utility of a proportion comes from the fact that if only one of the numbers is not known, it can easily be found. Suppose that two bombs are given, one weighing 450 pounds and the other weighing 150 pounds, and that the length of the first bomb is 36 inches. The length of bomb No. 2 is not known, but the length of any bomb is "proportional" to its weight, then

weight of bomb No.1 = weight of bomb No. 1 {{over}}
weight of bomb No.2 = length of bomb No. 2
is the proportion expressing this face. Now some of these quantities are known:

450 lb = 36 in. {{over}}
150 lb length of bomb No. 2
Therefore, if the proportion is true then the length of bomb No. 2 must be 12 inches.

d. In mathematics, not only are symbols such as +,-,=, etc. used to simplify writing, but is also convenient to introduce other symbols whenever they will shorten the work. Thus, to continue the preceding example, let

w1=weight of bomb No. 1
w2=weight of bomb No. 2