Solve the following word problem. A fish is swimming at −10.8%0D%0A−%0D%0A10.8%0D%0A 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%0D%0A−%0D%0A37.8%0D%0A meters? Show your work and write a sentence to explain what your answer means. how many min
To find out how long it will take for the fish to reach a depth of −37.8 meters, we need to find how many times it descends 1.5 meters and then multiply that by 2 (since it descends 1.5 meters every 2 minutes).
First, we need to find the distance the fish needs to descend from −10.8 meters to −37.8 meters: 37.8 - 10.8 = 27 meters.
Next, we divide the distance by the descent rate to find how many times the fish needs to descend: 27 / 1.5 = 18.
Finally, we multiply the number of descents by the time it takes for each descent: 18 * 2 = <<18*2=36>>36 minutes.
Therefore, it will take the fish 36 minutes to reach a depth of −37.8 meters.
This means that the fish will swim downward for 36 minutes and reach a depth of −37.8 meters below sea level.
To find out how long it will take for the fish to reach a depth of -37.8 meters, we can set up an equation.
Let's assume t represents the time in minutes it takes for the fish to reach -37.8 meters.
The initial depth of the fish is -10.8 meters, and every 2 minutes it descends another 1.5 meters. So, after t minutes, it would have descended (1.5 * t) meters.
Therefore, the equation can be written as:
-10.8 - (1.5 * t) = -37.8
To solve this equation, we need to isolate the variable t.
First, add 10.8 to both sides:
-1.5 * t = -37.8 + 10.8
-1.5 * t = -27
Next, divide both sides by -1.5:
t = -27 / -1.5
t = 18
Therefore, it will take 18 minutes for the fish to reach a depth of -37.8 meters.
In simpler terms, the fish descends 1.5 meters every 2 minutes, so after 18 minutes it would have descended 9 * 1.5 = 13.5 meters. Starting from an initial depth of -10.8 meters, it would reach a depth of -37.8 meters.
To solve this word problem, we can use a simple formula:
Time = Distance/Rate
In this case, the initial depth of the fish is -10.8 meters and it descends 1.5 meters every 2 minutes. We need to find out how long it takes for the fish to reach a depth of -37.8 meters.
First, we can calculate the difference in depth between the initial depth and the desired depth:
Difference in Depth = Final Depth - Initial Depth
Difference in Depth = -37.8 meters - (-10.8 meters)
Difference in Depth = -37.8 meters + 10.8 meters
Difference in Depth = -27 meters
Next, we divide the difference in depth by the rate at which the fish descends per minute:
Time = Difference in Depth / Rate
Time = -27 meters / (-1.5 meters/2 minutes)
To simplify the calculation, we can divide both the numerator and denominator by 0.5:
Time = -27 meters / (-1.5 meters/2 minutes)
Time = -27 meters / (-0.75 meters/minute)
Time = (-27 meters) * (2 minutes / -0.75 meters)
Now, we can cancel out the meters in the numerator and denominator:
Time = -27 * 2 / -0.75
Time = 54 / -0.75
Dividing 54 by -0.75:
Time ≈ -72
The time it takes for the fish to reach a depth of -37.8 meters is approximately -72 minutes.
Now, let's explain the answer:
The negative sign in the answer (-72 minutes) indicates that the fish is moving downwards, as expected since it's descending. The absolute value of 72 minutes tells us the time it takes for the fish to reach the desired depth. However, keep in mind that negative time values don't have a physical meaning in this context. In practical terms, we can say it takes approximately 72 minutes for the fish to reach a depth of 37.8 meters below sea level.