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 find out how long it will take for the fish to reach a depth of -37.8 meters, we need to determine the total depth the fish needs to descend from its starting depth of -10.8 meters to -37.8 meters.

  1. Calculate the total depth change required:

    \[ \text{Total depth change} = \text{Final depth} - \text{Starting depth} \] \[ \text{Total depth change} = -37.8 - (-10.8) \] \[ \text{Total depth change} = -37.8 + 10.8 = -27.0 \text{ meters} \]

    The fish needs to descend 27.0 meters.

  2. Determine the rate of descent:

    The fish descends 1.5 meters every 2 minutes. Therefore, we can calculate how many meters it descends in one minute:

    \[ \text{Rate of descent} = \frac{1.5 \text{ meters}}{2 \text{ minutes}} = 0.75 \text{ meters per minute} \]

  3. Calculate the time required to descend 27.0 meters:

    We can now find out how long it will take to descend that total depth:

    \[ \text{Time} = \frac{\text{Total depth change}}{\text{Rate of descent}} \] \[ \text{Time} = \frac{27.0 \text{ meters}}{0.75 \text{ meters per minute}} \] \[ \text{Time} = 36 \text{ minutes} \]

  4. Conclusion:

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

Final sentence: The fish will take 36 minutes to swim down from a depth of -10.8 meters to -37.8 meters, descending at a rate of 1.5 meters every 2 minutes.