Answer:
2 hours and 18 minutes.
Explanation:
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Currently, we have two separate stocks going at the same time, so I will isolate calculations based on each stock. For these two, I am going to be discussing the concept of fixed value and variable value.
A fixed value is something that cannot be changed due to any circumstances. A good example of this is the starting value or starting balance of something. The reason why is because you will always have that value in your calculation.
A variable value is something that can be changed due to quantity. A good example of this is usually a value accompanied with some sort of quantity that changes the total of said value.
Now that we have the concepts out of the way, we can now begin to solve.
Stock A:
What we know from Stock A is that the price at 9AM is $15.88 and it increases at a rate of $0.08 each hour. In this stock, we note that the fixed value here is $15.88 because it is assumed that this is what we started off with, and a variable value of $0.08 each hour. Since the price increases, we would have to add whatever variable price we get with whatever fixed price we have. We can actually turn this into a formula! Here's how it would look like, we let y be the total price and we let x be the number of hours that has passed:
Stock B:
Now, we move onto Stock B. Stock B at noon starts at $16.63 and it decreases at a rate of $0.14 each hour. For this stock, we can say that the fixed value is $16.63 and we can say that the variable value is -$0.14 each hour. Now this formula is going to be different than the first one. Instead of the price increasing, it is going to be decreasing and that is why we put the negative. It means that we're going to have to take our total and subtract it by the variable value. The formula looks like this:
Something we need to do before answer:
Now, back in Stock B, I highlighted over the noon part. Why is that the case? Because the times for both stocks are different in terms of starting time. We need to match up the times before we even begin any calculations. From 9AM to noon, that is 3 hours so what we can do is use the formula and calculate the new total for when Stock A reaches noon and that would look like this:
So, our new total for Stock A would be $16.12, when it reaches noon. Now we can get to figuring out how many hours it will take for the prices of the two stocks to be the same. The new formula of Stock A looks like this:
Answer Time:
In order to figure out how many hours it takes for the prices to be the same, we can do something called solving for systems of equation. We have our formulas for both stocks as such:
Since x is what we want to solve for, we can substitute y in equation 1 for equation 2. So, what we get is this:
And now, we solve for x as such:
- Moving like terms over to right and left sides.
- Evaluating them.
Alright! Now, we can prove that by plugging in that x value and getting the total value of both:
Stock A:
Stock B:
In my calculation, this is the closest that the prices can meet. So, it would take about 2 hours and 18 minutes. If the answer is wrong or if there are any questions, let me know!