Question

Challenge The price of Stock A at 9 A.M. was $13.45. Since then, the price has been increasing at the rate of $0.08 each hour. At noon the price of Stock B was $14.20. It begins to decrease at the rate

of $0.14 each hour. If the two rates continue, in how many hours will the prices of the two stocks be the same?
In about hours, the prices of the two stocks will be the same.
(Round to the nearest tenth as needed.)

Answer 1

Approximately 2.3 hours after 12 noon

Explanation:

We are given
Stock A price at 9AM = $13.45
It increases by $0.08 per hour

Stock B at noon = $14.20
It decreases by $0.14 each hour

We have to find when the two prices will be the same.

Since the base time references are different - 9am for A and noon for B, we have to establish the same time reference

Let's do this by finding the price of stock A at noon, then we have the same time base reference of noon

9am - noon = 3 hours

In 3 hours stock A would have risen by 0.08 x 3 = $0.24

Price of stock A at noon is 13.45 + 0.24 = $13.69

Thereafter stock A continues to increase by the same rate of $0.08 per hour
The equation to model stock A price starting at noon is
13.69 + 0.08x where x is the number of hours elapsed after 12 noon

Stock B price is $14.20 at 12 noon and decreases by $0.14 per hour
Equation to model stock B price after 12 noon is

14.20 - 0.14x where x is the elapsed time after 12 noon

For both prices to be the same after the same x hours, we have
13.69 + 0.08x = 14.20 - 0.14x

Solving for x will tell us how many hours it will take for both stock prices to be the same

Solving
13.69 + 0.08x = 14.20 - 0.14x

• Subtract 13.69 from both sides:
  0.08x = 14.20 - 13.69 - 0.14x
  0.08x = 0.51 - 0.14x
  
• Add 0.14x to both sides:
  0.08x + 0.14x = 0.51
  0.22x = 0.51
  
• x = 0.51/0.22
  x = 2.318
  x = 2.3 rounded to nearest tenth

So the two stock prices will be the same 2.3 hours after 12 noon or about 2 hours and 18 minutes after 12 noon or roughly around 2:18pm

I got 18 minutes by multiplying 0.3 x 60 = 18