In the context of the problem you provided, the answer \( t = 7.5 \) represents the time in hours at which the temperatures of Station A and Station B will be equal.
To clarify:
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Equations:
- The temperature at Station A after \( t \) hours is given by \( T_A = 58 - 5t \).
- The temperature at Station B after \( t \) hours is given by \( T_B = -2 + 3t \).
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Setting the equations equal: By solving the equation \( 58 - 5t = -2 + 3t \), you found \( t = 7.5 \).
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Interpretation of \( t = 7.5 \):
- This means that after 7.5 hours, the temperatures of both stations will be the same.
- It does NOT mean that the temperature will be 7.5 degrees Fahrenheit; rather, it means the temperature of both stations will equal each other at that specific time.
To find the actual temperature at that time, you would substitute \( t = 7.5 \) back into either temperature equation:
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For Station A: \[ T_A = 58 - 5(7.5) = 58 - 37.5 = 20.5 \text{ degrees Fahrenheit} \]
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For Station B: \[ T_B = -2 + 3(7.5) = -2 + 22.5 = 20.5 \text{ degrees Fahrenheit} \]
Thus, after 7.5 hours, both stations will reach the same temperature of 20.5 degrees Fahrenheit.
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