A 100 gallon tank is being drained at a rate of 5 gallons per minute. A second tank containing 10 gallons of water is being filled at a rate of 4 gallons per minute. Can you find out when the two tanks will have the same amount of water in them?
find t such that
100-5t = 10+4t
Yes, I can help you find out when the two tanks will have the same amount of water in them.
To solve this problem, we need to set up an equation to represent the rate at which the water is changing in each tank.
Let's define:
x = the number of minutes it takes for the two tanks to have the same amount of water.
The rate at which the first tank is changing is -5 gallons per minute, since it is being drained.
The rate at which the second tank is changing is +4 gallons per minute, since it is being filled.
So, the equation representing the change in the amount of water in the two tanks over time is:
100 - 5x = 10 + 4x
To find the value of x when the two tanks have the same amount of water, we can solve this equation.
First, let's simplify it:
100 - 5x = 10 + 4x
Combining like terms, we get:
5x + 4x = 100 - 10
Simplifying further, we have:
9x = 90
Dividing both sides of the equation by 9, we get:
x = 10
Therefore, the two tanks will have the same amount of water after 10 minutes.