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.
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.
To solve this problem, we can use the formula:
Time = (Final Depth - Initial Depth) / Descent Rate
In this case, the initial depth is -10.8 meters, the final depth is -37.8 meters, and the descent rate is 1.5 meters every 2 minutes.
First, we calculate the difference in depth:
Depth difference = -37.8 meters - (-10.8 meters)
= -37.8 meters + 10.8 meters
= -27 meters
Next, we substitute these values into the formula:
Time = (-27 meters) / (1.5 meters/2 minutes)
= (-27 meters) / (0.75 meters/minute)
= (-27 meters) * (2/0.75) minutes
= (-27 meters) * (8/3) minutes
= -216/3 minutes
= -72 minutes
Therefore, it will take the fish 72 minutes to reach a depth of -37.8 meters.
The negative sign indicates that the fish is swimming below sea level since the initial depth is negative. Thus, the answer means that it will take 72 minutes for the fish to reach a depth of -37.8 meters below sea level.
To solve this word problem, we need to find out how long it will take for the fish to reach a depth of -37.8 meters, starting from -10.8 meters, descending 1.5 meters every 2 minutes.
First, let's calculate the total distance the fish needs to descend:
Total descent = Final depth - Initial depth
Total descent = -37.8 meters - (-10.8 meters)
Total descent = -37.8 meters + 10.8 meters
Total descent = -27 meters
Next, let's calculate how many intervals of 2 minutes it will take to cover this total descent:
Number of intervals = Total descent / Descent per interval
Number of intervals = -27 meters / -1.5 meter per interval
Number of intervals = 18 intervals
Now, to find the total time, we need to multiply the number of intervals by the interval time:
Total time = Number of intervals * Interval time
Total time = 18 intervals * 2 minutes per interval
Total time = 36 minutes
Therefore, it will take the fish 36 minutes to reach a depth of -37.8 meters.
In plain English, this means that if a fish starts swimming at -10.8 meters and descends 1.5 meters every 2 minutes, it will take 36 minutes for the fish to reach a depth of -37.8 meters below sea level.
To find the time it will take for the fish to reach a depth of -37.8 meters, we need to set up an equation.
Let's assume the time it takes for the fish to reach a depth of -37.8 meters is t minutes.
In 2 minutes, the fish descends 1.5 meters. So, in t minutes, it will descend (1.5 * t) meters.
Using this information, we can set up the following equation:
-10.8 + (1.5 * t) = -37.8
To isolate t, we can first subtract -10.8 from both sides:
1.5 * t = -37.8 - (-10.8)
1.5 * t = -37.8 + 10.8
1.5 * t = -27
Next, we can divide both sides of the equation by 1.5:
t = -27 / 1.5
t = -18
Therefore, it will take the fish 18 minutes to reach a depth of -37.8 meters.
This means that after swimming for 18 minutes, the fish will descend from -10.8 meters to -37.8 meters.