Tank A contains 35 gallons of water and is increasing at a rate of 5 gallons per minute.
Tank B contains 100 gallons of water and is decreasing at a rate of 8 gallons per minute.
a) In how many minutes will the tanks contain the same amount of water?
b) How much water will that be?
a) Let's represent the amount of minutes as 't'.
In t minutes, the amount of water in Tank A will be 35 + 5t.
In t minutes, the amount of water in Tank B will be 100 - 8t.
To find when the tanks contain the same amount of water, we need to solve the equation:
35 + 5t = 100 - 8t
Adding 8t to both sides:
35 + 13t = 100
Subtracting 35 from both sides:
13t = 65
Dividing both sides by 13:
t = 5
Therefore, the tanks will contain the same amount of water in 5 minutes.
b) To find out how much water that would be, we can substitute t into either tank's equation. Let's use Tank A:
Amount of water in Tank A = 35 + 5t
Amount of water in Tank A = 35 + 5(5)
Amount of water in Tank A = 35 + 25
Amount of water in Tank A = 60
Therefore, the tanks will contain 60 gallons of water when they have the same amount.
To solve this problem, we can set up two equations to represent the situation:
For Tank A: A(t) = 35 + 5t
For Tank B: B(t) = 100 - 8t
Where A(t) represents the amount of water in Tank A after t minutes, and B(t) represents the amount of water in Tank B after t minutes.
a) To find the point at which both tanks contain the same amount of water, we need to find the time t when A(t) = B(t):
35 + 5t = 100 - 8t
Rearranging the equation:
13t = 65
Dividing both sides by 13:
t = 5
Therefore, the tanks will contain the same amount of water after 5 minutes.
b) To find the amount of water at this time, we substitute t = 5 into either equation:
A(5) = 35 + 5(5) = 35 + 25 = 60 gallons
Therefore, at this time, both Tank A and Tank B will contain 60 gallons of water.
To find out when the tanks contain the same amount of water and how much water that will be, we can set up a simple equation.
Let's assume t is the number of minutes it takes for the tanks to contain the same amount of water.
a) In how many minutes will the tanks contain the same amount of water?
To solve this, we need to set up an equation based on the information given.
In tank A, the water is increasing at a rate of 5 gallons per minute, so the amount of water in tank A after t minutes can be represented as 35 + 5t.
In tank B, the water is decreasing at a rate of 8 gallons per minute, so the amount of water in tank B after t minutes can be represented as 100 - 8t.
To find when the tanks contain the same amount of water, we set up the equation:
35 + 5t = 100 - 8t
Simplifying the equation, we get:
13t = 65
Dividing both sides by 13, we find:
t = 5
Therefore, it will take 5 minutes for the tanks to contain the same amount of water.
b) How much water will that be?
To find out how much water will be in the tanks after 5 minutes, we can substitute the value of t into either 35 + 5t or 100 - 8t, as they will be equal.
Substituting t = 5 into 35 + 5t:
35 + 5(5) = 35 + 25 = 60 gallons
Therefore, after 5 minutes, both tanks will contain 60 gallons of water.