Question

Write and solve an equation to solve the problem.
After a blizzard, 18 inches of snow sat on Maggie’s driveway. She measured the snow each
hour and determined that it was melting (decreasing) at a rate of 0.5 inches per hour.

Answer 1

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 \( t \):

1. Add \( 0.5t \) to both sides:
\[
18 = 0.5t
\]

2. Divide both sides by \( 0.5 \):
\[
t = \frac{18}{0.5}
\]

3. 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.