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 deep throat of -37.8 meters? Show your work and write a sentence to explain what you answer means.
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 needs to descend by 1.5 meters.
First, we find the difference in depth between the current 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 divide the difference by the descent rate of 1.5 meters per 2 minutes: -27 meters ÷ 1.5 meters = -18.
Therefore, the fish needs to descend 18 times in order to reach a depth of -37.8 meters.
Since the fish descends 1.5 meters every 2 minutes, it will take the fish 18 times 2 minutes = 36 minutes to reach a depth of -37.8 meters.
This means that it will take the fish 36 minutes to reach a depth of -37.8 meters.
why
The calculations show that it will take the fish 36 minutes to reach a depth of -37.8 meters because we divide the total depth difference (-27 meters) by the descent rate (1.5 meters per 2 minutes) to determine the number of times the fish needs to descend. Then, we multiply the number of descents needed by the time it takes for each descent (2 minutes per descent) to find the total time.
Can u show me the problem with numbers
Certainly! Here's the problem with numerical values:
Given:
Current depth: -10.8 meters
Target depth: -37.8 meters
Descent rate: 1.5 meters per 2 minutes
Step 1: Find the difference in depth
Depth difference = Target depth - Current depth
Depth difference = -37.8 meters - (-10.8 meters)
Depth difference = -37.8 meters + 10.8 meters
Depth difference = -27 meters
Step 2: Determine the number of descents needed
Number of descents = Depth difference / Descent rate
Number of descents = -27 meters / 1.5 meters
Number of descents = -18
Step 3: Calculate the total time
Total time = Number of descents * Time per descent
Total time = -18 * 2 minutes
Total time = -36 minutes
Therefore, it will take the fish 36 minutes to reach a depth of -37.8 meters.
Can u give me the whole equation smaller though
Certainly! Here's the equation in a shorter form:
Total time = (Target depth - Current depth) / Descent rate * Time per descent
Plugging in the known values:
Total time = (-37.8 meters - (-10.8 meters)) / 1.5 meters * 2 minutes
Simplifying:
Total time = (-27 meters) / 1.5 meters * 2 minutes
Total time = -18 * 2 minutes
Total time = -36 minutes
Therefore, it will take the fish 36 minutes to reach a depth of -37.8 meters.