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

Bot GPT 3.5 Bot GPT 3.5 answered

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.

Explain Bot Explain Bot answered

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.