Question

Fathom is a unit once used by sailors to measure the depth of water. If a sunken ship was located underwater at 240 feet, which expression would describe the location of the ship in fathoms?
1 fathom = 6 feet
A. $ 240 \times 6 $
B. $ 240 \div 6 $
C. $ 240 - 6 $
D. $ 240 + 6 $

Answer 1

Hint: Unitary method is an efficient method to solve this question. In the unitary method, we are first told to find the unit value using the multiple value, and then calculate the required value accordingly.
For instance, if 6 mangoes cost $ 12{\rm{ dollars}} $ , then what would be the cost of 7 mangoes?
Use a unitary method here i.e. find the value of mango by dividing the entire equation by 6. $ 6{\rm{ mangoes = 12 dollars}} $ , this means $ 1{\rm{ mango = }}\dfrac{{12}}{6} $ i.e. 2 dollars.
Hence, $ 7{\rm{ mangoes = 2}} \times 7{\rm{ dollars}} $ i.e. 14 dollars.

Complete step-by-step answer:
As per the question, it is given that
1 fathom = 6 feet.
Now, we should use a unitary method to find the value of 1 feet in terms of fathom.
1 fathom = 6 feet
Now, for finding the value of 1 feet, divide the entire equation by 6.
 $ \Rightarrow 1{\rm{ feet = }}\dfrac{1}{6}{\rm{ fathom}}......\left( 1 \right) $
Now, the ship has sunk to a depth of 240 feet underwater.
We have to convert 240 feet in terms of fathom.
According to the unitary method, we can now find the required value by multiplying the unit value.
240 feet is to be converted in fathom
 $ 240{\rm{ feet = 240 }} \times {\rm{ }}\left( {{\rm{1 feet}}} \right) $
Now, we can substitute equation (1) in the equation $ 240{\rm{ feet = 240 }} \times {\rm{ }}\left( {{\rm{1 feet}}} \right) $ .
 $
\Rightarrow 240{\rm{ feet = 240 }} \times {\rm{ }}\left( {\dfrac{{\rm{1}}}{6}{\rm{ fathom}}} \right)\\
 = \left( {240 \div 6} \right){\rm{ fathom}}
 $

So, the correct answer is “Option B”.

Note: Unitary method is simple to apply in the word problems. It is a method through which we can find the value of the required thing using the unit value of the product derived from the multiple value.