Use the equation to solve for t to find after how many hours the stations will be the same temperature.

Question

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

t
=

Answer 1

To find the time \( t \) at which the temperatures of Station A and Station B are the same, we can set their temperature equations equal to each other:

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

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

1. First, add \( 5t \) to both sides:

\[ 58 = -2 + 3t + 5t \] \[ 58 = -2 + 8t \]

2. Next, add 2 to both sides:

\[ 58 + 2 = 8t \] \[ 60 = 8t \]

3. Now, divide both sides by 8:

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

Thus, the stations will be the same temperature after \( t = 7.5 \) hours.