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

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

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 = (0.39)/(0.25)`

`x = 1.56`

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