To solve the problem, let's break it down step-by-step.
### Understanding the Equation
We are given the equation [tex]\( d = 5h \)[/tex], where:
- [tex]\( d \)[/tex] is the depth of snow in centimeters
- [tex]\( h \)[/tex] is the number of hours
- The constant 5 represents the rate of snow accumulation in centimeters per hour
### Part 1: How many hours does it take for 1 centimeter of snow to accumulate?
To find the number of hours [tex]\( h \)[/tex] for which 1 centimeter of snow accumulates:
1. We set [tex]\( d = 1 \)[/tex].
2. We then solve for [tex]\( h \)[/tex] in the equation [tex]\( 1 = 5h \)[/tex].
So, solving for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{1}{5} \][/tex]
[tex]\[ h = 0.2 \][/tex]
Therefore, it takes 0.2 hours for 1 centimeter of snow to accumulate.
### Part 2: How many centimeters of snow accumulate per hour?
From the given equation [tex]\( d = 5h \)[/tex]:
- We see that snow accumulates at a rate of 5 centimeters per hour.
So, the rate of snowfall is:
[tex]\[ 5 \text{ centimeters per hour} \][/tex]
### Summary
- How many hours does it take for 1 centimeter of snow to accumulate?
[tex]\[
0.2 \text{ hours}
\][/tex]
- How many centimeters of snow accumulate per hour?
[tex]\[
5 \text{ centimeters}
\][/tex]
This step-by-step approach allows us to understand and solve the problem using algebraic manipulation and comprehension of the provided equation.
