Math Problem Statement

At the beginning of a snowstorm, Connor had 11 inches of snow on his lawn. The snow then began to fall at a constant rate of 3 inches per hour. Assuming no snow was melting, how much snow would Connor have on his lawn 5 hours after the snow began to fall? How much snow would Connor have on his lawn after tt hours of snow falling?

Solution

To solve this, let's break it down into two parts:

Part 1: Snow after 5 hours

  • Initially, Connor had 11 inches of snow on his lawn.
  • Snow is falling at a rate of 3 inches per hour.
  • In 5 hours, the total snow from the storm would be 3×5=153 \times 5 = 15 inches.

So, the total amount of snow on the lawn after 5 hours would be the initial 11 inches plus the 15 inches of newly fallen snow: 11+15=26 inches11 + 15 = 26 \text{ inches} Thus, Connor would have 26 inches of snow on his lawn after 5 hours.

Part 2: Snow after tt hours

Let tt represent the number of hours the snow has been falling. The snow falls at 3 inches per hour, so after tt hours, the additional snow is 3t3t inches. Adding this to the initial 11 inches of snow gives the total snow after tt hours: Total snow=11+3t inches\text{Total snow} = 11 + 3t \text{ inches} Thus, after tt hours, Connor would have 11+3t11 + 3t inches of snow on his lawn.

Would you like further details or clarifications? Here are 5 related questions to deepen understanding:

  1. What would be the total snow after 8 hours of snowfall?
  2. If the rate of snowfall increased to 4 inches per hour, how much snow would be on the lawn after 5 hours?
  3. How long would it take for the total snow to reach 50 inches?
  4. If the snow was melting at 1 inch per hour while snow was still falling, what would be the total amount after 5 hours?
  5. How would the formula change if the snow started at a different initial amount, say 20 inches?

Tip: When solving word problems, it's helpful to first establish what quantities change and what remains constant. This makes it easier to set up equations.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Linear equations
Rates of change
Word problems

Formulas

Total snow after t hours = 11 + 3t

Theorems

-

Suitable Grade Level

Grades 6-8