Let's denote the amount of snow on Maggie's driveway after \( t \) hours as \( S(t) \). We know that initially, the snow was 18 inches deep. Since the snow is melting at a constant rate of 0.5 inches per hour, we can express the amount of snow at any time \( t \) with the following equation:
\[ S(t) = 18 - 0.5t \]
We want to find out how much snow will be left after a certain number of hours \( t \). However, we need to determine a specific time when all the snow has melted.
To find out when the snow completely melts (i.e., when \( S(t) = 0 \)), we set the equation to zero:
\[ 18 - 0.5t = 0 \]
Now we can solve for \( t \):
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Add \( 0.5t \) to both sides: \[ 18 = 0.5t \]
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Divide both sides by \( 0.5 \): \[ t = \frac{18}{0.5} \]
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Calculate: \[ t = 36 \]
Thus, the snow will completely melt after 36 hours.
In summary, the equation to determine the amount of snow over time is \( S(t) = 18 - 0.5t \), and the snow will completely melt in 36 hours.
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