Solve the following word problem. A fish is swimming at −10.8

meters, or 10.8 meters below sea level. Every 2 minutes it descends another 1.5 meters. How long will it take for the fish to reach a depth of −37.8
meters? Show your work and write a sentence to explain what your answer means.(4 points)

1 answer

To solve the problem, we can start by determining the total depth the fish needs to reach and how much distance it has left to descend.

  1. Current Depth: The fish is currently at -10.8 meters.
  2. Target Depth: The fish needs to reach -37.8 meters.

Next, we calculate the total distance it needs to descend:

\[ \text{Distance to descend} = \text{Target Depth} - \text{Current Depth} \] \[ = -37.8 - (-10.8) \] \[ = -37.8 + 10.8 \] \[ = -27.0 \text{ meters} \]

So, the fish needs to descend 27.0 meters.

  1. Descent Rate: The fish descends 1.5 meters every 2 minutes.

Next, we calculate how many 1.5 meter descents it will take to reach a total descend of 27.0 meters. We do this by dividing the total distance by the distance it descends each time:

\[ \text{Number of descents} = \frac{\text{Total Distance to Descend}}{\text{Distance Descent per Interval}} \] \[ = \frac{27.0}{1.5} \] \[ = 18 \text{ descents} \]

  1. Total Time: Since each descent takes 2 minutes, we can calculate the total time by multiplying the number of descents by the time per descent:

\[ \text{Total Time} = \text{Number of Descents} \times \text{Time per Descent} \] \[ = 18 \times 2 \] \[ = 36 \text{ minutes} \]

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

Explanation Sentence: The fish will take 36 minutes to descend from its current depth of 10.8 meters below sea level to a deeper depth of 37.8 meters below sea level.