To find out when the two containers hold the same amount of water, we need to set the two equations equal to each other:
16x + 104 = -2x^2 + 40x + 160
Rearranging and simplifying this equation gives us:
2x^2 - 24x - 56 = 0
Now we need to solve this quadratic equation for x. Factoring out a 2 from the equation gives:
2(x^2 - 12x - 28) = 0
(x - 14)(x + 2) = 0
So, we have two possible solutions for x: x = 14 or x = -2. Since time cannot be negative, we take x = 14 minutes.
To find out how much water the containers hold at this time, we substitute x = 14 into either equation. Let's use Container A's equation:
y = 16(14) + 104
y = 224 + 104
y = 328
Therefore, at the time when the containers hold the same amount of water (after 14 minutes), they both hold 328 ounces of water.
Water is added to two containers for 16 minutes. The equations below model the ounces of water, y, in each container after x minutes. At the time after the start when the containers hold the same amount of water, how much water do they hold? Container A : y=16x+104
Container B : y= -2x2 + 40x + 160
1 answer