A container has 300 liters of water, and a second container has 700 liters of water. The first container begins filling up at a rate of 5 liters per minute at the same time the second starts draining at a rate of 6 liters per minute. Which equation can be used to find the number of minutes, x, that elapse before the two containers have the same amount of water?A container has 300 liters of water, and a second container has 700 liters of water. The first container begins filling up at a rate of 5 liters per minute at the same time the second starts draining at a rate of 6 liters per minute. Which equation can be used to find the number of minutes, x, that elapse before the two containers have the same amount of water?
300+5x = 700-6x
love the duplication. :-(
Let's define the amount of water in the first container after x minutes as W1 and the amount of water in the second container after x minutes as W2.
The rate at which the first container is filling up is 5 liters per minute, so the equation for the amount of water in the first container after x minutes is: W1 = 300 + 5x
The rate at which the second container is draining is 6 liters per minute, so the equation for the amount of water in the second container after x minutes is: W2 = 700 - 6x
To find the number of minutes, x, that elapse before the two containers have the same amount of water, we need to set W1 equal to W2 and solve for x:
300 + 5x = 700 - 6x
To find the number of minutes, x, that elapse before the two containers have the same amount of water, we can use the equation:
300 + 5x = 700 - 6x
Explanation:
Let's break down the equation step by step:
1. The initial amount of water in the first container is 300 liters, so we add 300 to the equation: 300 + (...)
2. The rate at which the first container is filling up is 5 liters per minute, so we add 5 times the number of minutes, x, to the equation: 300 + 5x + (...)
3. The initial amount of water in the second container is 700 liters, so we subtract 700 from the equation: 300 + 5x = 700 - (...)
4. The rate at which the second container is draining is 6 liters per minute, so we subtract 6 times the number of minutes, x, from the equation: 300 + 5x = 700 - 6x
Simplifying the equation:
Now, we can simplify the equation further:
300 + 5x = 700 - 6x
Combine like terms by adding 6x to both sides and subtracting 300 from both sides:
300 + 5x + 6x = 700 - 6x + 6x - 300
11x = 400
Divide both sides of the equation by 11:
11x/11 = 400/11
x = 400/11
So, the equation that can be used to find the number of minutes, x, that elapse before the two containers have the same amount of water is:
300 + 5x = 700 - 6x