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. Make the answer simple and short
To find the time it takes for the fish to reach a depth of -37.8 meters, we can set up an equation. Since the fish descends 1.5 meters every 2 minutes, we can divide the total change in depth (37.8 - 10.8 = 27) by the change in depth per time (1.5) to find the time it takes (27 / 1.5 = 18). Therefore, it will take the fish 18 minutes to reach a depth of -37.8 meters. This means that every 2 minutes, the fish descends 1.5 meters and after 18 minutes, it will have reached a depth of -37.8 meters.
To find the time it takes for the fish to reach a depth of -37.8 meters, we can subtract the initial depth of the fish (-10.8 meters) from the target depth (-37.8 meters).
-37.8 meters - (-10.8 meters) = -37.8 meters + 10.8 meters = -27 meters
Next, we divide the change in depth (-27 meters) by the rate of descent (1.5 meters per 2 minutes):
-27 meters ÷ 1.5 meters per 2 minutes = -18 minutes
Therefore, it will take the fish 18 minutes to reach a depth of -37.8 meters.
Explanation: This means that the fish will descend at a rate of 1.5 meters every 2 minutes until it reaches a depth of -37.8 meters, which will take a total of 18 minutes.
To solve this word problem, we can set up an equation. Let's assume that the time taken to reach a depth of -10.8 meters is t = 0.
The equation to represent the depth (d) of the fish at any given time (t) is:
d = -10.8 - 1.5t
We want to find out the time it takes for the fish to reach a depth of -37.8 meters. So, we set up the following equation:
-37.8 = -10.8 - 1.5t
By rearranging this equation, we can solve for t:
-1.5t = -37.8 + 10.8
-1.5t = -27
Dividing both sides of the equation by -1.5:
t = 18
Therefore, it will take the fish 18 minutes to reach a depth of -37.8 meters.
In simple terms, it means that the fish will descend at a rate of 1.5 meters every 2 minutes, starting from -10.8 meters, and it will reach a depth of -37.8 meters after 18 minutes.