Final answer:
The prices of Stock A and Stock B will be the same approximately 4.3 hours after 9 AM (about 1:20 PM), considering that Stock A is increasing by $0.13 each hour from $12.82 and Stock B is decreasing by $0.14 each hour from $13.57 starting at noon.
Step-by-step explanation:
The solution to this problem involves finding the point at which the price of Stock A is equal to that of Stock B, given their respective rates of change over time. Stock A starts at $12.82 at 9 AM and increases at the rate of $0.13 each hour. Stock B is priced at $13.57 at noon and decreases at $0.14 per hour. To find out when the prices will be the same, we set up the equations based on their rates of change and solve for the time when their prices are equal.
Let t be the number of hours after 9 AM for Stock A and the number of hours after noon for Stock B. The price of Stock A after t hours is modeled by the equation A(t) = 12.82 + 0.13t. The price of Stock B after t hours is modeled by the equation B(t) = 13.57 - 0.14(t - 3), since Stock B starts changing three hours later at noon.
To find when A(t) equals B(t), we set the two equations equal to each other and solve for t:
12.82 + 0.13t = 13.57 - 0.14(t - 3)
This simplifies to:
0.13t + 0.14t = 13.57 - 12.82 + 0.42
0.27t = 1.17
t = 1.17 / 0.27
t ≈ 4.33 hours
So, the prices of the two stocks will be the same in approximately 4.3 hours after 9 AM, which translates to around 1:20 PM.