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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)
To solve this problem, we can use the formula:
Time = (Final Depth - Initial Depth) / Rate of Descent
Given:
Initial Depth = -10.8 meters
Final Depth = -37.8 meters
Rate of Descent = 1.5 meters every 2 minutes
Plugging the values into the formula:
Time = (-37.8 - (-10.8)) / 1.5
Simplifying the equation:
Time = (-37.8 + 10.8) / 1.5
Time = -27 / 1.5
Time = -18 minutes
Since time cannot be negative in this context, the negative sign is ignored, and the answer is 18 minutes.
So, it will take the fish 18 minutes to reach a depth of -37.8 meters.
Can you write it in a simpler form?
Certainly!
The fish descends 1.5 meters every 2 minutes. To reach a depth of -37.8 meters from -10.8 meters, we can calculate their difference divided by the rate of descent.
(-37.8 - (-10.8)) / 1.5 simplifies to -27 / 1.5.
This evaluates to -18, which means it will take the fish 18 minutes to reach a depth of -37.8 meters.