The total height of the piling is calculated by finding the common denominator and setting up an equation with the given fractions representing parts of the piling. Solving for the total height gives a result of 504 feet.
The puzzle states that a piling supporting a bridge divides into three parts: one part submerged in sand, one part in the water, and one part above water in the air. Let's denote the total height of the piling as H. According to the puzzle, 1/3 of the piling is in the sand, 120 feet is in the water, and 3/7 of the piling is in the air. To find the total height, we need to consider that the piling is divided into parts that represent fractions of the total height. We can express the section in the water as a fraction of the total height as well.
Firstly, we can calculate the remaining fraction of the piling that is not in the air:
1 - 3/7 = 4/7 of the piling
Since 1/3 is in the sand and the rest is in the water, we can express this as:
1/3 + (120/H) = 4/7
After rearranging, we get:
120/H = 4/7 - 1/3 = 12/21 - 7/21 = 5/21
Therefore:
120 = (5/21) * H
Hence:
H = 120 * (21/5)
H = 504 feet
Thus, the total height of the piling is 504 feet.