QuestionSkylar starts with 8 inches of snow. If it snows 1.5 inches/hour, how much snow after 4 hours and $t$ hours?

Studdy Solution

STEP 1

Assumptions1. The initial amount of snow on the lawn is8 inches. . The rate of snowfall is constant at1.5 inches per hour.
3. No snow is melting during this period.
4. We are asked to find the total amount of snow after4 hours and after $t$ hours.

STEP 2

First, we need to find the amount of snow that falls in a given period of time. We can do this by multiplying the rate of snowfall by the time.
$Snowfall\, amount = Rate\, of\, snowfall \\times Time$

STEP 3

Now, plug in the given values for the rate of snowfall and time ( hours) to calculate the snowfall amount.
$Snowfall\, amount =1.5\, inches/hour \\times\, hours$

STEP 4

Calculate the snowfall amount.
$Snowfall\, amount =1.\, inches/hour \\times4\, hours =6\, inches$

STEP 5

Now that we have the snowfall amount, we can find the total amount of snow on the lawn. This includes both the initial amount and the snowfall amount.
$Total\, snow = Initial\, snow + Snowfall\, amount$

STEP 6

Plug in the values for the initial snow and the snowfall amount to calculate the total snow.
$Total\, snow =8\, inches +6\, inches$

STEP 7

Calculate the total snow on the lawn.
$Total\, snow =\, inches +6\, inches =14\, inches$

STEP 8

Now, we need to find the amount of snow on the lawn after $t$ hours. We can use the same formula as before, but replace the time with $t$ .
$Snowfall\, amount = Rate\, of\, snowfall \\times Time$ $Snowfall\, amount =1.5\, inches/hour \\times t\, hours$

STEP 9

We can then find the total amount of snow on the lawn after $t$ hours by adding the initial amount of snow to the snowfall amount.
$Total\, snow = Initial\, snow + Snowfall\, amount$ $Total\, snow =8\, inches +.5\, inches/hour \\times t\, hours$

STEP 10

This is the general formula for the total amount of snow on the lawn after $t$ hours.
$Total\, snow =8\, inches +.5\, inches/hour \\times t\, hours$ So, Skylar would have14 inches of snow on her lawn4 hours after the snow began to fall and $8 +.5t$ inches of snow after $t$ hours of snow falling.

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