RF = 1:20,000
MD = 5 inches
x = GD
Solution: 1:20,000 :: 5:x
Using the rule of the means' product divided by the known extreme (1), find the unknown extreme (x),
which, in this case, represents the GD.
(5 x 20,000)/1 = 100,000
The answer is given in inches, which should be converted to the more conventional surveyor's units:
yards, feet, meters, or miles. This requires that you divide the answer by 36, 12, 39.37, or 63,360,
respectively.
e. The use of ratios and proportions can also serve you in other situations. See the following example:
Example: If a survey line measures 7,920 feet on the ground, what is the length of it on a map having a
RF of 1:31,680? Set up your proportion using the RF formula (RF = MD/GD). Since the MD is usually
expressed in inches, change the GD to inches by multiplying by 12. Let x equal the unknown mean.
RF = 1:31,680 (scale of progress map)
GD = 7,920 feet (length of surveyed line)
x = MD
Solution:
1:31,680 :: x:7,920 12
1:31,680 :: x:95,040
Using the rule of the extremes' product divided by the known mean (31,680), find the unknown mean
(x), which, in this case, represents the desired MD.
(1 x 95,040) /31,680 = 3 inches
f. Up to this point, only direct proportion has been discussed. In a direct proportion, both ratios
are direct ratios; that is, they increase or decrease in the same manner. In the map proportion problem
above, the first ratio (1:31,680) increased in the same manner as the second ratio (3:95,040). This
problem would also be a direct proportion if the terms had decreased in a like manner. Most of the
proportion problems you will use are direct proportions and, unless specifically noted, will be treated as
such. A simple clue that will aid you is to analyze each problem carefully to determine whether the
unknown term will be greater or lesser than the known term of the ratio in which it occurs. Thus, each
direct proportion takes the following pattern:
EN0591
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