A bank on an excavation site has a 3 to 1 slope; how many inches per foot will the bank rise?

A bank on an excavation site has a 3 to 1 slope; how many inches per foot will the bank rise?

• A. 3 inches per foot
• B. 4 inches per foot
• C. 5 inches per foot
• D. 6 inches per foot

Answer: (B)

In a 3 to 1 slope, the ratio indicates that for every 3 horizontal units (in this case, inches), there is a rise of 1 vertical unit (inches) of height. To find out how many inches per foot (which is 12 inches) the slope rises, you can use the slope ratio directly. Since the slope is defined as "3 horizontal units for every 1 vertical unit," it can also be understood in terms of the total rise over run. If you look at this slope over 12 horizontal inches (1 foot), you can determine how many vertical inches the bank rises. For a complete horizontal run of 12 inches: - Using the slope, you would have: \[ \text{Vertical rise} = \frac{1 \text{ unit rise}}{3 \text{ units run}} \times 12 \text{ inches run} = \frac{12}{3} = 4 \text{ inches rise} \] Therefore, the bank rises 4 inches for every foot of horizontal distance, corresponding to the correct answer. This effectively means that the bank is about 4 inches above the starting point for each foot you measure horizontally, confirming that

In a 3 to 1 slope, the ratio indicates that for every 3 horizontal units (in this case, inches), there is a rise of 1 vertical unit (inches) of height. To find out how many inches per foot (which is 12 inches) the slope rises, you can use the slope ratio directly.

Since the slope is defined as "3 horizontal units for every 1 vertical unit," it can also be understood in terms of the total rise over run. If you look at this slope over 12 horizontal inches (1 foot), you can determine how many vertical inches the bank rises.

For a complete horizontal run of 12 inches:

• Using the slope, you would have:

[

\text{Vertical rise} = \frac{1 \text{ unit rise}}{3 \text{ units run}} \times 12 \text{ inches run} = \frac{12}{3} = 4 \text{ inches rise}

]

Therefore, the bank rises 4 inches for every foot of horizontal distance, corresponding to the correct answer. This effectively means that the bank is about 4 inches above the starting point for each foot you measure horizontally, confirming that