Question

Sailors once used a unit of length called a fathom to measure the depth of the water. Each fathom is equal to 6 feet. Which equation represents the relationship between x, the depth of water in fathoms, and y, the depth of the water in feet?

Answer 1

y = x*(6 feet/1 fathom)

Explanation:

We know the relation:

1 fathom = 6 feet.

We can write:

1 = (6 feet/1 fathom)

Now, remember that any number multiplied by 1 does not change.

Then suppose that we have a measure of 3 fathoms, then:

3 fathoms = (3 fathoms)*1

= (3 fathoms)*((6 feet/1 fathom)) = (3 fathoms/1 fathom)*(6feet)

= 3*(6 feet) = 18 feet.

So we changed the units by multiplying the original measure by (6 feet/1 fathom)

Then, if x is the depth of water in fathoms and y is the depth of the water in feet, we can write:

y = x*(6 feet/1 fathom)