Question

The price of Stock A at 9 A.M. was ​$.14.57 Since​ then, the price has been increasing at the rate of ​$0.08 each hour. At noon the price of Stock B was ​$15.07. It begins to decrease at the rate of ​$0.14 each hour. If the two rates​ continue, in how many hours will the prices of the two stocks be the​ same?

Answer 1

The prices of Stock A and Stock B will be the same approximately 2.27 hours after 9 A.M. for Stock A (around 11:16 A.M.) and after noon for Stock B (around 2:16 P.M.).

Step-by-step explanation:

The equal price point between Stock A and Stock B will be found by setting up and solving a linear equation based on their rates of change. Stock A starts at $14.57 at 9 A.M. and increases by $0.08 each hour. Stock B is at $15.07 at noon and decreases by $0.14 each hour.

To find when the stock prices will be the same, we can use the following equation:
14.57 + 0.08t = 15.07 - 0.14t, where 't' is the number of hours after 9 A.M. for Stock A and after noon for Stock B.

First, combine like terms:
0.08t + 0.14t = 15.07 - 14.570.22t = 0.50

Now, divide both sides by 0.22 to find 't':
t = 0.50 / 0.22t ≈ 2.27 hours

After calculating, we find that the prices of Stock A and Stock B will be the same approximately 2.27 hours after 9 A.M. for Stock A, which translates to around 11:16 A.M., and after noon for Stock B, which translates to around 2:16 P.M.