Use the table to estimate. About when will the stations be the same temperature? In other words, after about how many hours will Station A be the same temperature as Station B?

Question

Station A's temperature after t hours: 58+(−5t)
Station B's temperature after t hours: −2+3t

Hours Station A's
temperature Station B's
temperature
0 58 -2
4 38 10
8 18 22
12 -2 34

Between 0 and 4

Between 8 and 12

Between 4 and 8

Answer 1

To determine when the temperatures at Station A and Station B will be the same, we can set the equations for their temperatures equal to each other and solve for \( t \):

Station A's temperature: \( T_A = 58 - 5t \)

Station B's temperature: \( T_B = -2 + 3t \)

Setting these equal:

\[ 58 - 5t = -2 + 3t \]

Now, we can solve for \( t \):

1. Add \( 5t \) to both sides:

\[ 58 = -2 + 8t \]

2. Add 2 to both sides:

\[ 60 = 8t \]

3. Divide by 8:

\[ t = \frac{60}{8} = 7.5 \]

So the temperatures at Station A and Station B will be the same after \( 7.5 \) hours.

Now, let's analyze the answer choices to see where this time falls:

• Between 0 and 4 hours, the temperatures are not equal.
• Between 4 and 8 hours, the temperatures are not equal.
• Between 8 and 12 hours, the temperatures are also not equal.

Thus, the temperatures at both stations will be the same after approximately 7.5 hours, which falls in the range between 4 and 8 hours.