A proportion is a statement of equality between two ratios. If the value of one ratio is equal to the value of another ratio, they are said to be in proportion. For example, the ratio 3:6 is equal to the ratio 4:8. Therefore, this can be written 3:6 :: 4:8 or 3:6 4:8. In any proportion, the first and last terms are called the extremes; the second and third terms are called the means (fig. 2).

Figure 2. Terms of proportion.

17. Rules of Proportion

There are three rules of proportion that are used in determining an unknown quantity.

Example: The weight of 15 feet of iron pipe is 8 pounds.

What is the weight of 255 feet of
the same pipe? Let the un-
known quantity be repre-
sented by the letter y. Since
ratios must express a relation
between quantities of the same
kind, one ratio must be be-
tween feet and feet and the
other between pounds and
pounds.

Study the problems; 255 feet
of pipe will weigh more than
15 feet of pipe. Arrange the
first ratio in the order LES-
SER to GREATER-15 feet:
15
255*

255 feet, or

Example 1: A pulley 30 inches in diameter is turning at a speed of 300 revolutions per minute. If this pulley is belted to a pulley 15 inches in diameter (fig. 3), determine the speed at which the smaller pulley is turning.

Let the speed of the smaller pulley be represented by y. Study the problem; the first ratio will be between inches and the second will be between revolutions per minute (rpm). Also note that the second pulley is smaller than the first and must make more revolutions than the first. Therefore, the answer will be a number larger than 300. Arrange the ratios in the order LESSER to GREATER.

a. The ratio 2:3 is the inverse of the ratio 3:2. In proportion, when a second ratio is equal to the inverse of the first ratio, the elements are said to be inversely proportional.

b. Two numbers are inversely proportional when one increases as the other decreases. In this case, their product is always the same. In problems dealing with pulleys, the speeds of different size pulleys connected by belts are inversely proportional to their diameters. A smaller pulley rotates faster than a larger pulley.

to complete the same job, considering that they will work at the same speed?

c. If 3 resistors cost 25 cents, find the cost of 60 resistors at the same rate?

d. If the upkeep on 62 trucks for a year is $3,100, what would be the upkeep on 28 such trucks for 1 year at the same rate?

e. At a given temperature, the resistance of a wire increases with its length. If the resistance of a wire per 1,000 feet at 68°F is .248 ohm, what is the resistance of 1,500 feet; of 1,200 feet; of 1,850 feet; of 3,600 feet?

f. If 21-gage wire weighs 2.452 pounds per 1,000 feet, what is the weight of 1,150 feet; 1,540 feet; 1,680 feet; 349 yards?

g. The speeds of gears running together are inversely proportional to the number of teeth in the gears. A driving gear with 48 teeth meshes with a driven gear with 16 teeth. If the driving gear turns at the rate of 100 rpm, how many rpm are made by the driven gear?

h. A 36-tooth gear running at a speed of 280 rpm drives another gear with 64 teeth. What is the speed of the other gear?