Question

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. At noon the price of Stock B was ​$13.70. It begins to decrease at the rate of ​$0.13 each hour. If the two rates​ continue, in how many hours will the prices of the two stocks be the​ same?

Answer 1

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:

$S_{A}(x) = 12.95 + 0.12x$

After noon:

Noon is 3 hours after 9 AM, so

$S_{A}(3) = 12.95 + 0.12*3 = 13.31$

So in x hours after noon, the value is given by:

$S_{A}(x) = 13.31 + 0.12x$

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:

$S_{B}(x) = 13.70 - 0.13x$

In how many hours will the prices of the two stocks be the​ same?

This is x for which:

$S_{A}(x) = S_{B}(x)$

$13.31 + 0.12x = 13.70 - 0.13x$

$0.25x = 0.39$

$x = \frac{0.39}{0.25}$

$x = 1.56$

The prices of the two stocks will be the same in 1.56 hours.