Question

The price of Stock A at 9 A.M. was ​$12.63. Since​ then, the price has been increasing at the rate of ​$0.08 each hour. At noon the price of Stock B was ​$13.13. It begins to decrease at the rate of ​$0.15 each hour. If the two rates​ continue, in how many hours will the prices of the two stocks be the​ same?

Answer 1

1.13 hours after 12 noon or 4.13 hours after 9 A.M.

1:08 P.M. (rounded to the nearest minute)

Explanation:

To determine when the prices of the two stocks will be the same, we can set up equations for each stock's price as a function of time, t.

Let t represent the time in hours after 12 noon.

Stock A

The price of Stock A at 9 A.M. was $12.63, and it increases at the rate of $0.08 each hour. Therefore, at 12 noon it will be $12.87. So, the price of Stock A t hours after 12 noon can be represented as:

`A(t) = 12.87 + 0.08t`

Stock B

The price of Stock B at noon was $13.13, and it decreases at the rate of $0.15 each hour. So, the price of Stock B t hours after noon. can be represented as:

`B(t) = 13.13 - 0.15t`

To find when the prices of the two stocks will be the same, we need to set A(t) equal to B(t) and solve for t:

`\begin{aligned}12.87 + 0.08t&= 13.13 - 0.15t\\12.87 + 0.08t+0.15t &= 13.13 - 0.15t+0.15t\\12.87 + 0.23t &= 13.13\\12.87 + 0.23t-12.87 &= 13.13-12.87\\0.23t&=0.26\\t&=1.13043478...\end{aligned}`

Therefore, it will take approximately 1.13 hours after 12 noon for the prices of Stock A and Stock B to be the same. This translates to the time 1:08 P.M. (rounded to the nearest minute).