Now that we’ve estimated when the stations will be the same temperature, let’s find the exact answer. You can set the expressions for Station A’s temperature and Station B’s temperature equal to one another to write an equation that represents the two stations being at an equal temperature. Do that now.

Question

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

=

Station A's temperature
Station B's temperature

Answer 1

To find when the temperatures at Station A and Station B are equal, we need to set their temperature expressions equal to each other.

The temperature at Station A after \( t \) hours is given by: \[ 58 - 5t \]

The temperature at Station B after \( t \) hours is given by: \[ -2 + 3t \]

Set these two expressions equal to each other: \[ 58 - 5t = -2 + 3t \]

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 both sides by \( 8 \): \[ t = \frac{60}{8} = 7.5 \]

So, the two stations will be at the same temperature after \( 7.5 \) hours.