Solve the following word problem, a shark is swimming at -14.2 m or 14.2 m below sea level every five minutes it distance another 1.2 m how long will it take the shark to reach -23.8 m or 23.8 m below sea level show your work and write a sentence to explain what your answer means.
To find how long it will take the shark to reach -23.8 m below sea level, we need to determine how many times the shark needs to swim downward by 1.2 m.
The difference in distance between -14.2 m and -23.8 m is 23.8 - 14.2 = 9.6 m.
To travel a distance of 9.6 m, the shark needs to swim downward 9.6 ÷ 1.2 = 8 times.
Since the shark swims downward every five minutes, it will take the shark 8 × 5 = 40 minutes to reach -23.8 m or 23.8 m below sea level.
This means it will take the shark 40 minutes to swim from its starting point at -14.2 m to a depth of -23.8 m below sea level.
To find out how long it will take the shark to reach -23.8 m below sea level, we can set up an equation.
Let's denote the time in minutes as "t" and the distance below sea level as "d."
Given:
Initial depth: -14.2 m
Rate of descent: 1.2 m every 5 minutes
Target depth: -23.8 m
The equation we can form is:
-14.2 + (1.2/5)t = -23.8
First, let's simplify the equation:
-14.2 + 0.24t = -23.8
Next, let's isolate "t":
0.24t = -23.8 + 14.2
0.24t = -9.6
Now, divide both sides of the equation by 0.24:
t = -9.6 / 0.24
t = -40
Therefore, the shark will take 40 minutes to reach a depth of -23.8 m below sea level.
Explanation:
The negative sign indicates that the shark is descending below sea level. The time it takes for the shark to reach -23.8 m below sea level is 40 minutes. This means that after 40 minutes of continuous descent, the shark will achieve a depth of -23.8 m below sea level.
To solve this word problem, we need to determine how many times the shark has to travel a distance of 1.2 m to reach a total depth of -23.8 m.
First, let's calculate the difference between the initial depth and the target depth:
Difference in depth = -23.8 m - (-14.2 m)
= -23.8 m + 14.2 m
= -9.6 m
Next, let's divide the difference in depth by the distance the shark covers in each swim:
Number of swims = Difference in depth / Distance covered per swim
= -9.6 m / 1.2 m
= -8
Since the number of swims cannot be negative, we take the absolute value of the result, which gives us 8.
Now, let's multiply the number of swims by the time it takes for each swim:
Total time = Number of swims × Time per swim
= 8 × 5 minutes
= 40 minutes
Therefore, it will take the shark 40 minutes to reach a depth of -23.8 m (-23.8 m below sea level).
In summary, the shark needs to swim 8 times, with each swim taking 5 minutes, to reach a total depth of -23.8 m. The total time required is 40 minutes.