QuestionA fish starts at -10.8 m and descends 1.5 m every 2 min. How long to reach -37.8 m? Show your work and explain.

Studdy Solution

STEP 1

Assumptions1. The initial depth of the fish is -10.8 meters. . The fish descends at a rate of1.5 meters every minutes.
3. We need to find out how long it will take for the fish to reach a depth of -37.8 meters.

STEP 2

First, we need to find out how much further the fish needs to descend to reach -37.8 meters. We can do this by subtracting the initial depth from the final depth.
$Additional\, depth = Final\, depth - Initial\, depth$

STEP 3

Now, plug in the given values for the initial depth and final depth to calculate the additional depth.
$Additional\, depth = -37.8\, meters - (-10.8\, meters)$

STEP 4

Calculate the additional depth.
$Additional\, depth = -37.8\, meters - (-10.8\, meters) = -27\, meters$

STEP 5

Now that we have the additional depth, we can find out how long it will take for the fish to descend this much. We know that the fish descends1.5 meters every2 minutes, so we can find the time by dividing the additional depth by the rate of descent.
$Time = Additional\, depth / Rate\, of\, descent$

STEP 6

Plug in the values for the additional depth and the rate of descent to calculate the time.
$Time = -27\, meters /1.5\, meters\, per\,2\, minutes$

STEP 7

Calculate the time in minutes.
$Time = -27\, meters /1.5\, meters\, per\,2\, minutes = -36\, minutes$

STEP 8

Since time cannot be negative, we take the absolute value of the time to get the actual time it will take for the fish to reach a depth of -37.8 meters.
$Time = |-36\, minutes| =36\, minutes$ The fish will take36 minutes to reach a depth of -37.8 meters.

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