Question

A fish is swimming at a location of -9.5 meters, or 9.5 meters below sea level. Every 3 minutes it descends 1.5 meters. How long will it take to reach a depth of --24.5 meters?

Answer 1

To determine how long it will take for the fish to reach a depth of -24.5 meters, we first need to identify how far the fish needs to descend from its current depth of -9.5 meters.

1. **Calculate the total descent required:**
\[
\text{Depth to reach} = -24.5 \text{ meters}
\]
\[
\text{Current depth} = -9.5 \text{ meters}
\]
\[
\text{Descent required} = -24.5 - (-9.5) = -24.5 + 9.5 = -15 \text{ meters}
\]

So, the fish needs to descend 15 meters.

2. **Calculate the rate of descent:**
The fish descends 1.5 meters every 3 minutes.

3. **Calculate how many 3-minute intervals are needed to descend 15 meters:**
To find out how many intervals are needed, we divide the total descent by the distance descended in each interval:
\[
\text{Intervals} = \frac{\text{Descent required}}{\text{Descent per interval}} = \frac{15 \text{ meters}}{1.5 \text{ meters}} = 10 \text{ intervals}
\]

4. **Calculate the total time needed:**
Since each interval takes 3 minutes, the total time required is:
\[
\text{Total time} = 10 \text{ intervals} \times 3 \text{ minutes per interval} = 30 \text{ minutes}
\]

Thus, it will take the fish **30 minutes** to reach a depth of -24.5 meters.