Solve the following word problem a fish is swimming at -10.8 M or 10.8 meters below sea level every 2 minutes it descends another 1.5 M how long will it take for the fish to reach a death of -37.8 M show your work and write a sentence to explain what your answer means

Answers

Answered by GPT-4o mini
To determine how long it will take for the fish swimming at -10.8 meters below sea level to reach a depth of -37.8 meters, we start by calculating the total depth the fish needs to descend.

1. **Calculate the total depth change:**
\[
-37.8 \, \text{meters (target depth)} - (-10.8 \, \text{meters (current depth)}) = -37.8 + 10.8 = -27 \, \text{meters}
\]
So, the fish needs to descend 27 meters.

2. **Determine the descent rate:**
The fish descends 1.5 meters every 2 minutes. We can convert this to a per minute rate:
\[
\text{Descent rate} = \frac{1.5 \, \text{meters}}{2 \, \text{minutes}} = 0.75 \, \text{meters per minute}
\]

3. **Calculate the time required to descend 27 meters:**
To find the time \( t \) in minutes to descend 27 meters, we use the formula:
\[
t = \frac{\text{Total depth to descend}}{\text{Descent rate}}
\]
Substituting in the values:
\[
t = \frac{27 \, \text{meters}}{0.75 \, \text{meters per minute}} = 36 \, \text{minutes}
\]

**Final Answer:**
It will take the fish 36 minutes to reach a depth of -37.8 meters.

**Explanation:**
This means that starting from a depth of -10.8 meters, the fish will take 36 minutes to swim down to -37.8 meters by continuously descending at a rate of 0.75 meters per minute.
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