A diver had descended 64 feet underwater after 4 minutes. After 6 minutes, the diver had descended 96 feet under water.

Question

What is the constant of proportionality that relates the number descended y to the number of minutes x
A. 3/2
B. 1/16
C. 24
D. 16

Answer 1

To determine the constant of proportionality, we can set up the relationship of depth (\(y\)) to time (\(x\)) based on the information given.

From the problem:

• At \(x = 4\) minutes, \(y = 64\) feet.
• At \(x = 6\) minutes, \(y = 96\) feet.

First, let's find the rate of descent per minute between these two points:

1. Calculate the change in depth: \[ \text{Change in } y = 96 - 64 = 32 \text{ feet} \]

2. Calculate the change in time: \[ \text{Change in } x = 6 - 4 = 2 \text{ minutes} \]

3. Now, find the rate of descent (constant of proportionality): \[ \text{Rate} = \frac{\text{Change in } y}{\text{Change in } x} = \frac{32 \text{ feet}}{2 \text{ minutes}} = 16 \text{ feet per minute} \]

Thus, the constant of proportionality that relates the depth descended (\(y\)) to the time in minutes (\(x\)) is \(16\).

So, the answer is D. 16.