Final answer:
The prices of Stock A and Stock B will be the same approximately 4.81 hours after 9 A.M., or around 1:49 P.M.
Step-by-step explanation:
To determine in how many hours the prices of Stock A and Stock B will be the same, we need to set up equations for their prices and find when they are equal. At 9 A.M., Stock A was at $14.93 and has been increasing at $0.07 each hour. At noon, Stock B was at $15.43 and began to decrease at $0.09 each hour.
Let x be the number of hours after 9 A.M. Then the price of Stock A after x hours will be 14.93 + 0.07x dollars. Since Stock B starts at noon, which is 3 hours after 9 A.M., we consider the hours for Stock B as x-3. Therefore, the price of Stock B after x hours will be 15.43 - 0.09(x-3).
To find when the prices are the same, we set the equations equal to each other and solve for x:
14.93 + 0.07x = 15.43 - 0.09(x-3)
Simplifying this equation gives us:
14.93 + 0.07x = 15.43 - 0.09x + 0.27
Combining like terms, we get:
0.07x + 0.09x = 15.43 + 0.27 - 14.93
0.16x = 0.77
So, x = 0.77 / 0.16
x ≈ 4.8125
Since we started at 9 A.M., after approximately 4.81 hours the prices will be the same, which will be around 1:49 P.M.