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 out how long it will take for the fish to reach a depth of -37.8 meters, we need to find the number of times the fish will descend 1.5 meters until it reaches -37.8 meters.
First, we calculate the difference in depth between -37.8 meters and -10.8 meters:
-37.8 - (-10.8) = -37.8 + 10.8 = -27
Next, we divide the difference in depth by the descent rate of 1.5 meters per 2 minutes:
-27 / 1.5 = -18
The fish will descend 1.5 meters every 2 minutes, so it will take it 2 minutes to descend 1.5 meters. Therefore, it will take the fish 2 minutes * 18 = 36 minutes to reach a depth of -37.8 meters.
In conclusion, it will take the fish 36 minutes to reach a depth of -37.8 meters, descending 1.5 meters every 2 minutes.
in the smallest answer for kids
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 equation:
Depth = Starting Depth + (Rate of Descent × Time)
Let's denote the starting depth as D_start = -10.8 meters.
The rate of descent is R_descent = -1.5 meters every 2 minutes.
The desired depth is D_desired = -37.8 meters.
We want to find the time it will take for the fish to reach the desired depth, so we can rearrange the equation as follows:
Time = (Depth - Starting Depth) / Rate of Descent
Time = (D_desired - D_start) / R_descent
Substituting the given values, we have:
Time = (-37.8 - (-10.8)) / -1.5
Time = (-37.8 + 10.8) / -1.5
Time = -27 / -1.5
Time = 18 minutes
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, so after 18 minutes it will have descended a total of 27 meters.
To solve this word problem, we need to find out how many 1.5-meter descents the fish needs to reach a depth of −37.8 meters.
First, let's calculate the difference in depth between the fish's starting point and the target depth:
Difference in depth = target depth - starting depth
= -37.8 meters - (-10.8 meters)
= -37.8 meters + 10.8 meters
= -27 meters
Since the fish descends 1.5 meters every 2 minutes, we can find out how many 1.5-meter descents are required to cover the remaining depth:
Number of descents = (Difference in depth) / (Descent per minute)
= (-27 meters) / (1.5 meters per descent)
= -27 meters / 1.5 meters per descent
≈ -18 descents
We have calculated that the fish needs approximately -18 descents. However, since we cannot have a negative number of descents, we can interpret this as the fish needing 18 descents in total.
To find the time it takes for the fish to reach the target depth, we need to multiply the number of descents by the time it takes for each descent:
Time = Number of descents * Time per descent
= 18 descents * 2 minutes per descent
= 36 minutes
Therefore, it will take the fish approximately 36 minutes to reach a depth of −37.8 meters.
In summary, the fish will take around 36 minutes to reach a depth of −37.8 meters, descending 1.5 meters every 2 minutes. The answer means that the fish needs to descend 18 times to reach the target depth, with each descent taking 2 minutes.