Math Problem Statement

Snow is falling steadily in Syracuse, New York. After 2 hours, 4 inches of snow has fallen. Complete the table to show how many inches of snow would fall if it continues to snow at the same rate.

Solution

The problem is asking to determine how much snow will fall at different times, given a steady rate of snowfall. We are told that 4 inches of snow has fallen after 2 hours.

From this information, we can calculate the rate of snowfall. The rate of snowfall is:

Rate=4 inches2 hours=2 inches per hour\text{Rate} = \frac{4 \text{ inches}}{2 \text{ hours}} = 2 \text{ inches per hour}

Now, let's complete the table based on this constant rate of 2 inches per hour.

Table Completion:

  1. Time = 1 hour: Using the rate of 2 inches per hour, after 1 hour, the snow fallen will be: Snow=2×1=2 inches\text{Snow} = 2 \times 1 = 2 \text{ inches}

  2. Time = 2 hours: This is already provided in the problem. After 2 hours, 4 inches of snow has fallen.

  3. Time = 6.5 hours: We can calculate the amount of snow after 6.5 hours by using the same rate: Snow=2×6.5=13 inches\text{Snow} = 2 \times 6.5 = 13 \text{ inches}

  4. Time = xx hours: For a general value of xx, the snow fallen will be: Snow=2×x inches\text{Snow} = 2 \times x \text{ inches}

So the completed table should be:

Time (hours)Snow (inches)
12
24
6.513
xx2x2x

Would you like any further details on this? Here are some related questions for you:

  1. How would the snowfall change if the rate increased to 3 inches per hour?
  2. What is the total snow after 10 hours at the same rate?
  3. How would you calculate the snow fallen if the rate was unknown but the final snow height was given?
  4. How can you verify that the snowfall is indeed constant?
  5. If the rate were to change after 3 hours, how would that affect the table?

Tip: Always identify the rate of change when solving problems involving steady rates or linear relationships!

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Math Problem Analysis

Mathematical Concepts

Algebra
Rates
Proportional Relationships

Formulas

Rate of snowfall = (Total snow)/(Total time)
Total snow = Rate of snowfall × Time

Theorems

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Suitable Grade Level

Grades 6-8