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 find how long it will take for the fish to reach a depth of -37.8 meters, we need to determine how many times the fish will descend 1.5 meters.
First, we calculate the difference between the initial depth of the fish (-10.8 meters) and the target depth (-37.8 meters):
-37.8 meters - (-10.8 meters) = -37.8 meters + 10.8 meters = -27 meters.
Next, we divide the difference by the rate at which the fish descends:
-27 meters ÷ 1.5 meters/2 minutes = -27 meters ÷ 0.75 meters/minute = -36 minutes.
Therefore, it will take the fish 36 minutes to reach a depth of -37.8 meters below sea level.
Answer: It will take the fish 36 minutes to reach a depth of -37.8 meters.
To solve this problem, we need to find out how many 2-minute intervals it will take for the fish to descend from -10.8 meters to -37.8 meters.
The fish descends 1.5 meters every 2 minutes. We can set up an equation to represent the situation:
-10.8 meters + (1.5 meters/2 minutes) * x = -37.8 meters
Simplifying the equation:
-10.8 + 0.75x = -37.8
Next, subtract -10.8 from both sides of the equation:
-0.75x = -37.8 + 10.8
-0.75x = -27
To isolate x (number of intervals), we divide both sides of the equation by -0.75:
x = -27 / -0.75
x = 36
Therefore, it will take the fish 36 intervals of 2 minutes each to reach a depth of -37.8 meters.
To explain the answer: The fish descends 1.5 meters every 2 minutes. After 36 intervals of 2 minutes, the fish would have descended 36 * 1.5 = 54 meters, reaching a depth of -37.8 meters from its initial position of -10.8 meters.
To solve this word problem, you need to find out how many times the fish descends by 1.5 meters until it reaches a depth of -37.8 meters.
First, we need to calculate the difference between the initial depth (-10.8 meters) and the target depth (-37.8 meters):
-37.8 meters - (-10.8 meters) = -37.8 meters + 10.8 meters = -27 meters.
Next, we need to divide the difference by the rate at which the fish descends:
-27 meters / 1.5 meters per 2 minutes = -18.
This means that the fish will need to descend 18 times, each time by 1.5 meters, to reach a depth of -37.8 meters. Since each descent takes 2 minutes, the total time it will take for the fish to reach that depth is:
18 descents x 2 minutes per descent = 36 minutes.
Therefore, it will take the fish 36 minutes to reach a depth of -37.8 meters.
To summarize: It will take the fish approximately 36 minutes to swim from a depth of -10.8 meters to a depth of -37.8 meters, descending 1.5 meters every 2 minutes.