Question

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

1 answer

To solve this problem, we need to first determine how much deeper the fish needs to descend to reach a depth of -37.8 meters from its current depth of -10.8 meters.

  1. Calculate the distance the fish needs to descend: \[ \text{Depth difference} = \text{Final depth} - \text{Current depth} \] \[ \text{Depth difference} = -37.8 - (-10.8) = -37.8 + 10.8 = -27 , \text{meters} \]

    So, the fish needs to descend 27 meters to reach -37.8 meters.

  2. Determine how many 1.5 meter descents it takes to cover 27 meters: Since the fish descends 1.5 meters every 2 minutes, we can find the number of descents needed: \[ \text{Number of descents} = \frac{\text{Total descent needed}}{\text{Descent per interval}} = \frac{27}{1.5} = 18 \]

  3. Calculate the total time taken for these descents: Since each descent takes 2 minutes: \[ \text{Total time} = \text{Number of descents} \times \text{Time per descent} = 18 \times 2 = 36 , \text{minutes} \]

  4. Conclusion: The fish will take 36 minutes to reach a depth of -37.8 meters.

In summary, starting from -10.8 meters, it will take the fish 36 minutes to descend to -37.8 meters by swimming down 1.5 meters every 2 minutes.