Challenge The price of Stock A at 9 AM. was $15.93. Since then, the price has been increasing at the rate of $0.09 each hour. At noon the price of Stock B was $16.68. 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?

hours = $0.75 / $0.22
hours = 3.4091

We can’t have a fraction of an hour, so we need to round up. Therefore, it will take approximately 4 hours for the prices of the two stocks to be the same.

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saimaabdullatif008 saimaabdullatif008 · Answer 2 · 2024-02-24T20:16:41+01:00

Answer:

To find out when the prices of Stock A and Stock B will be the same, we can set up equations for each stock's price and then solve for the time when they are equal.

Let's denote:

[tex] P_A \: as \: the \: price \: of \: Stock \: A \\

P_B \: as \: the \: price \: of \: Stock \: B \\

t \: as \: the \: number \: of \: hours \: since \: 9 AM[/tex]

For Stock A, the price increases by $0.09 each hour, so the equation representing its price at any given time is:

[tex]\[ P_A = 15.93 + 0.09t \][/tex]

For Stock B, the price decreases by $0.13 each hour, so the equation representing its price at any given time is:

[tex]\[ P_B = 16.68 - 0.13t \][/tex]

To find when the prices are equal, we set the two equations equal to each other and solve for t

[tex]\[ 15.93 + 0.09t = 16.68 - 0.13t \]

Now, we solve for t : \\

\[ 0.09t + 0.13t = 16.68 - 15.93 \] \\

\[ 0.22t = 0.75 \] \\

\[ t = \frac{0.75}{0.22} \] \\

\[ t \approx 3.41 \] \\ [/tex]

So, in approximately 3.41 hours after 9 AM, the prices of Stock A and Stock B will be the same. Since we can't have a fraction of an hour, we round up to the nearest whole number. Therefore, it will take about 4 hours for the prices of the two stocks to be the same.