Final answer:
To find when the prices of Stock A and Stock B will be the same, equations representing their price changes are set equal to each other and solved for time, resulting in approximately 2.29 hours after noon, or around 2:17 P.M.
Step-by-step explanation:
To determine how many hours will pass before the prices of Stock A and Stock B are the same given their respective rates of increase and decrease, let us set up an equation to represent each stock's price over time.
Let x be the number of hours after 9 A.M. for Stock A and the number of hours after noon for Stock B.
The price of Stock A after x hours is given by the following equation:
Price of Stock A = 13.22 + 0.09x
The price of Stock B after x hours is given by the following equation:
Price of Stock B = 13.70 - 0.12x
Since we are looking for the time when the prices are the same, we set the equations equal to each other:
13.22 + 0.09x = 13.70 - 0.12x
Combining like terms, we get:
0.09x + 0.12x = 13.70 - 13.22
Simplifying the equation further, we find:
0.21x = 0.48
Dividing both sides by 0.21 to solve for x gives us:
x = 0.48 / 0.21
Calculating the value of x results in:
x ≈ 2.29 hours
Since Stock B starts changing at noon, 2.29 hours after noon would be the time the prices are the same, approximately at 2:17 P.M.