Splitting the height of the piling in water, air and sand is an illustration of the use of fractions
The height of the piling is 396 feet.
Let
[tex]W_f \to[/tex] Fraction in water
[tex]W_s \to[/tex] Fraction in sand
[tex]W_a \to[/tex] Fraction in air
[tex]H \to[/tex] Height of the piling
So, we have:
[tex]W_s = \frac 12[/tex]
[tex]W_a = \frac 3{11}[/tex]
First, we calculate the fraction in water using:
[tex]W_f + W_s + W_a= 1[/tex]
So, we have:
[tex]W_f + \frac 12 + \frac 3{11}= 1[/tex]
Collect like terms
[tex]W_f = 1 - \frac 12 - \frac 3{11}[/tex]
Take LCM
[tex]W_f = \frac {22 - 11 - 6}{22}[/tex]
[tex]W_f = \frac {5}{22}[/tex]
From the question, we understand that: 90 feet is in water.
This means that:
[tex]W_f \times H = 90[/tex]
So, we have:
[tex]\frac 5{22} \times H = 90[/tex]
Solve for H
[tex]H = \frac{90 \times 22}{5}[/tex]
[tex]H = 396[/tex]
Hence, the height of the piling is 396 feet.
Read more about fractions at:
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