Even seconds after a deep sea diver jumps into the ocean he is 69 feet below sea level and 28 seconds later, he is 195 feet below sea level. If he is descending under water at a constant rate, how many feet below sea level will he be 1.5 minutes after his initial descent?

Answer

To solve the problem step-by-step, we will follow these steps:

### Step 1: Determine the initial and final depths
The diver is initially at a depth of 69 feet below sea level. After 28 seconds, he is at a depth of 195 feet below sea level.

### Step 2: Calculate the change in depth
To find the change in depth, we subtract the initial depth from the final depth:
\[ \text{Change in depth} = \text{Final depth} - \text{Initial depth} = 195 \text{ feet} - 69 \text{ feet} = 126 \text{ feet} \]

### Step 3: Calculate the rate of descent
The rate of descent can be calculated using the formula:
\[ \text{Rate of descent} = \frac{\text{Change in depth}}{\text{Time}} = \frac{126 \text{ feet}}{28 \text{ seconds}} = 4.5 \text{ feet per second} \]

### Step 4: Convert time from minutes to seconds
We need to find out how deep the diver will be after 1.5 minutes. First, we convert 1.5 minutes into seconds:
\[ 1.5 \text{ minutes} = 1.5 \times 60 \text{ seconds} = 90 \text{ seconds} \]

### Step 5: Calculate the total distance descended in 1.5 minutes
Now, we can calculate the total distance the diver descends in 90 seconds using the rate of descent:
\[ \text{Distance descended} = \text{Rate of descent} \times \text{Time} = 4.5 \text{ feet per second} \times 90 \text{ seconds} = 405 \text{ feet} \]

### Step 6: Calculate the final depth after 1.5 minutes
To find the final depth after 1.5 minutes, we add the distance descended to the initial depth:
\[ \text{Final depth} = \text{Initial depth} + \text{Distance descended} = 69 \text{ feet} + 405 \text{ feet} = 474 \text{ feet} \]

Thus, the diver will be **474 feet below sea level** after 1.5 minutes.

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