a fire engine's water tank holds 1000 gallons of water. if the pump removes 300 gallons of water in 3 minutes, what is the change in the amount of water in the gallons in 1 minute?
Sure! Let's break it down into smaller steps:
Step 1: Set up the problem
- The fish is swimming at a depth of -15.2 meters below sea level.
- The fish descends another 2.5 meters every 3 minutes.
- We need to find out how long it will take for the fish to reach a depth of -45.2 meters.
Step 2: Calculate the difference in depth
- Initial depth: -15.2 meters
- Final depth: -45.2 meters
- Difference in depth: -45.2 meters - (-15.2 meters) = -30 meters
Step 3: Determine the change in depth per minute
- The fish descends 2.5 meters every 3 minutes.
- Change in depth per minute: 2.5 meters / 3 minutes = (5/2) meters per minute = 2.5/3 meters per minute.
Step 4: Set up the equation
- Let t represent the time in minutes it takes for the fish to reach -45.2 meters.
- We can use the formula: change in depth = rate of change * time
- Change in depth: -30 meters
- Rate of change: 2.5/3 meters per minute
- Equation: -30 meters = (2.5/3 meters per minute) * t
Step 5: Solve for t
- Multiply both sides of the equation by 3/2: (-30 meters)*(3/2) = (2.5/3 meters per minute) * t * (3/2)
- Simplify: -45 = (2.5/2) * t
- Multiply both sides of the equation by 2/2: (-45)*(2/2) = (2.5/2) * t * (2/2)
- Simplify: -90 = 2.5 * t
- To find t, divide both sides of the equation by 2.5: t = -90 / 2.5
- Simplify: t = -36
Step 6: Interpret the result
- It will take the fish 36 minutes to reach a depth of -45.2 meters.
To find the change in the amount of water in one minute, we need to determine how many gallons are removed in one minute.
First, we can figure out the gallons per minute rate by dividing the amount of water removed in 3 minutes (300 gallons) by 3:
300 gallons / 3 minutes = 100 gallons/minute
Therefore, the change in the amount of water in the tank in one minute is 100 gallons.
solve the following word problem. A fish is swimming at -15.2 meters, or 15.2 meters below sea level. every 3 minutes it descends another 2.5 meters. How long will it take for the fish to reach a depth f -45.2 meters?
To find out how long it will take for the fish to reach a depth of -45.2 meters, we can set up an equation.
Let's denote t as the time in minutes it takes for the fish to reach -45.2 meters.
Initially, the fish is already at -15.2 meters, so the difference in depth is:
-45.2 meters - (-15.2 meters) = -45.2 meters + 15.2 meters = -30 meters.
We know that every 3 minutes, the fish descends 2.5 meters. Thus, the change in depth per minute is:
2.5 meters / 3 minutes = (5/2) meters per minute = 2.5/3 meters per minute.
We can now set up an equation:
-30 meters = (2.5/3 meters per minute) * t.
To isolate t, we multiply both sides of the equation by 3/2:
-30 meters * (3/2) = (2.5/3 meters per minute) * t * (3/2).
Simplifying:
-45 = (2.5/2) * t.
To solve for t, we can multiply both sides of the equation by 2/2:
(-45)*(2/2) = (2.5/2) * t * (2/2).
-90 = 2.5 * t.
Finally, to find t, we divide both sides of the equation by 2.5:
t = -90 / 2.5.
Simplifying:
t = -36.
Therefore, it will take the fish 36 minutes to reach a depth of -45.2 meters.
Okay, now simplify the whole thing and break it down into small steps
Okay, now simplify and break it down into small steps
Sure! Let's break it down into smaller steps:
Step 1: Determine the initial depth
- The fish is currently swimming at a depth of -15.2 meters below sea level.
Step 2: Determine the desired depth
- The fish wants to reach a depth of -45.2 meters.
Step 3: Calculate the difference in depth
- The difference in depth is determined by subtracting the initial depth from the desired depth.
- -45.2 meters - (-15.2 meters) = -45.2 meters + 15.2 meters = -30 meters.
Step 4: Determine the rate of descent
- The fish descends another 2.5 meters every 3 minutes.
Step 5: Calculate the change in depth per minute
- To find the change in depth per minute, divide the rate of descent by the time interval.
- 2.5 meters / 3 minutes = 0.8333 meters per minute (rounded to four decimal places).
Step 6: Set up the equation
- Let t represent the time in minutes it takes for the fish to reach the desired depth.
- The equation can be written as: -30 meters = 0.8333 meters per minute * t.
Step 7: Solve for t
- Isolate t by dividing both sides of the equation by 0.8333: -30 meters / 0.8333 meters per minute = t.
- The resulting value for t is approximately 36.0024 minutes (rounded to four decimal places).
Step 8: Interpret the result
- It will take approximately 36.0024 minutes (or 36 minutes and 0.0144 seconds, rounded to four decimal places) for the fish to reach a depth of -45.2 meters.
Okay, now simplify and break that down into small steps...
Sure, let's break it down into smaller steps:
Step 1: Identify the initial and desired depth
- The fish is currently at a depth of -15.2 meters below sea level.
- The desired depth is -45.2 meters.
Step 2: Calculate the difference in depth
- The difference in depth is obtained by subtracting the initial depth from the desired depth.
- (-45.2 meters) - (-15.2 meters) = -45.2 meters + 15.2 meters = -30 meters.
Step 3: Determine the rate of descent
- The fish descends 2.5 meters every 3 minutes.
Step 4: Calculate the change in depth per minute
- Divide the rate of descent by the time interval to find the change in depth per minute.
- 2.5 meters / 3 minutes = 0.8333 meters per minute (rounded to four decimal places).
Step 5: Set up the equation
- Let t represent the time in minutes for the fish to reach the desired depth.
- The equation can be written as: -30 meters = 0.8333 meters per minute * t.
Step 6: Solve for t
- Divide both sides of the equation by 0.8333 to solve for t.
- (-30 meters) / (0.8333 meters per minute) = t.
- The resulting value for t is approximately 36.0024 minutes (rounded to four decimal places).
Step 7: Interpret the result
- It will take approximately 36.0024 minutes (or 36 minutes and 0.0144 seconds, rounded to four decimal places) for the fish to reach a depth of -45.2 meters.
To find the change in the amount of water in gallons per minute, we need to calculate the rate at which water is being removed from the tank.
Given that the pump removes 300 gallons of water in 3 minutes, we can start by finding the rate of water removal per minute.
To do this, we can set up a proportion:
300 gallons / 3 minutes = X gallons / 1 minute
By cross-multiplying, we can find the value of X (the number of gallons being removed per minute):
3 * X = 300 * 1
3X = 300
Dividing both sides by 3:
X = 100
Therefore, the pump removes 100 gallons of water per minute. This represents the change in the amount of water in the fire engine's tank in gallons per minute.