Question

a scuba diver descends farther down into the ocean from an initial depth of 13.6 feet below sea level. the scuba diver descends at a constant rate for 2 1/2 minutes and reaches a depth no more than 48.2 feet below sea level. what is the maximum rate, r, that the scuba diver may descend?
options:
○ r ≥ 13.84
○ r ≤ 13.84
○ r ≥ 24.72
○ r ≤ 24.72

Explanation:

Step1: Define the problem

The initial depth is \( 13.6 \) feet, the time of descent is \( 2\frac{1}{2} = 2.5 \) minutes, and the maximum final depth is \( 48.2 \) feet. Let \( r \) be the rate of descent (in feet per minute). The total depth after descending is the initial depth plus the distance descended, which is \( \text{initial depth} + r \times \text{time} \leq \text{maximum final depth} \).

Step2: Set up the inequality

Substitute the known values into the inequality: \( 13.6 + 2.5r \leq 48.2 \).

Step3: Solve for \( r \)

First, subtract \( 13.6 \) from both sides: \( 2.5r \leq 48.2 - 13.6 \). Calculate the right - hand side: \( 48.2-13.6 = 34.6 \). Then, divide both sides by \( 2.5 \): \( r\leq\frac{34.6}{2.5} \). Calculate \( \frac{34.6}{2.5}=13.84 \). So the inequality for \( r \) is \( r\leq13.84 \).

Answer:

\( r\leq13.84 \) (the option with \( r\leq13.84 \))