Answer:
The prices of the two stocks will be the same in 1.56 hours.
Step-by-step explanation:
The price of Stock A at 9 A.M. was $12.95 Since then, the price has been increasing at the rate of $0.12 each hour.
This means that after x hours, the value of Stock A is:
![S_{A}(x) = 12.95 + 0.12x](https://tex.z-dn.net/?f=S_%7BA%7D%28x%29%20%3D%2012.95%20%2B%200.12x)
After noon:
Noon is 3 hours after 9 AM, so
![S_{A}(3) = 12.95 + 0.12*3 = 13.31](https://tex.z-dn.net/?f=S_%7BA%7D%283%29%20%3D%2012.95%20%2B%200.12%2A3%20%3D%2013.31)
So in x hours after noon, the value is given by:
![S_{A}(x) = 13.31 + 0.12x](https://tex.z-dn.net/?f=S_%7BA%7D%28x%29%20%3D%2013.31%20%2B%200.12x)
At noon the price of Stock B was $13.70. It begins to decrease at the rate of $0.13 each hour.
This means that after x hours, the value of Stock B is:
![S_{B}(x) = 13.70 - 0.13x](https://tex.z-dn.net/?f=S_%7BB%7D%28x%29%20%3D%2013.70%20-%200.13x)
In how many hours will the prices of the two stocks be the same?
This is x for which:
![S_{A}(x) = S_{B}(x)](https://tex.z-dn.net/?f=S_%7BA%7D%28x%29%20%3D%20S_%7BB%7D%28x%29)
![13.31 + 0.12x = 13.70 - 0.13x](https://tex.z-dn.net/?f=13.31%20%2B%200.12x%20%3D%2013.70%20-%200.13x)
![0.25x = 0.39](https://tex.z-dn.net/?f=0.25x%20%3D%200.39)
![x = \frac{0.39}{0.25}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B0.39%7D%7B0.25%7D)
![x = 1.56](https://tex.z-dn.net/?f=x%20%3D%201.56)
The prices of the two stocks will be the same in 1.56 hours.