What is the slope of the pool bottom when the depth transitions from 3 feet to 8 feet over a distance of 40 feet?

To determine the slope of the pool bottom in this scenario, one must first calculate the total change in depth and the distance over which that change occurs. The depth transitions from 3 feet to 8 feet, resulting in a vertical change of 5 feet (8 feet - 3 feet). The distance over which this depth change occurs is 40 feet. The slope is defined as the vertical change divided by the horizontal distance over which that change occurs.

Calculating the slope involves using the formula:

[

\text{Slope} = \frac{\text{Vertical Change}}{\text{Horizontal Distance}} = \frac{5 \text{ feet}}{40 \text{ feet}}.

]

When you perform this calculation, you simplify the fraction:

[

\frac{5}{40} = \frac{1}{8} \text{ feet per foot}.

]

This fraction represents the slope in feet. To convert this value to inches, knowing that there are 12 inches in a foot, you multiply by 12, arriving at:

[

\frac{1}{8} \text{ feet/foot} \times 12 \text{ inches/foot} = 1.5 \text{ inches