challenge: the price of stock a at 9 a.m. was $14.45. since then, the price has been increasing at the rate…

challenge: the price of stock a at 9 a.m. was $14.45. since then, the price has been increasing at the rate of $0.05 each hour. at noon the price of stock b was $15.20. it begins to decrease at the rate of $0.11 each hour. if the two rates continue, in how many hours will the prices of the two stocks be the same? in about hours, the prices of the two stocks will be the same. (round to the nearest tenth as needed.)

challenge: the price of stock a at 9 a.m. was $14.45. since then, the price has been increasing at the rate of $0.05 each hour. at noon the price of stock b was $15.20. it begins to decrease at the rate of $0.11 each hour. if the two rates continue, in how many hours will the prices of the two stocks be the same? in about hours, the prices of the two stocks will be the same. (round to the nearest tenth as needed.)

Answer

Explanation:

Step1: Calculate the initial - time difference

From 9 A.M. to noon, there are 3 hours.

Step2: Set up the equation for stock prices

Let (t) be the number of hours after noon when the prices are the same. The price of Stock A is (P_A=14.45 + 0.05\times(3 + t)), and the price of Stock B is (P_B = 15.20-0.11t).

Step3: Set (P_A = P_B) and solve for (t)

[ \begin{align*} 14.45+0.05\times(3 + t)&=15.20 - 0.11t\ 14.45+0.15+0.05t&=15.20 - 0.11t\ 14.6+0.05t&=15.20 - 0.11t\ 0.05t+0.11t&=15.20 - 14.6\ 0.16t&=0.6\ t&=\frac{0.6}{0.16}=\frac{60}{16}= 3.75 \end{align*} ]

Answer:

3.8