If rain is falling at 0.5 inches per hour and 1.5 inches have already accumulated, how many hours must have passed if there are 5 inches of rain? Create a linear equation that is a model for the rain that has accumulated. Select the two correct answers.
1.5 + 0.5x = 5
To solve this problem, let's define the variables:
- r: rate of rain (0.5 inches per hour)
- a: amount of rain accumulated (in inches)
We want to find the number of hours (h) it takes for the amount of rain accumulated (a) to reach 5 inches.
Since the rain is falling at a constant rate, we can create a simple linear equation to model the situation:
a = r * h
In this equation, a represents the amount of rain accumulated, r represents the rate of rain, and h represents the number of hours.
Given that 1.5 inches of rain have already accumulated, we can plug in the values to find the equation for the amount of rain accumulated:
1.5 = 0.5 * h
Now, let's solve for h:
1.5 / 0.5 = h
h = 3
Therefore, it must have taken 3 hours for the amount of rain accumulated to reach 1.5 inches.
To solve this problem, let's create a linear equation to model the rain that has accumulated. We know that rain is falling at a rate of 0.5 inches per hour. Let's represent the number of hours that have passed as 'x', and the amount of rain accumulated as 'y'.
We can determine the equation by using the slope-intercept form, which is given by:
y = mx + b
where 'm' is the slope and 'b' is the y-intercept.
In this case, the slope represents the rate of rainfall, which is 0.5 inches per hour. So, the equation becomes:
y = 0.5x + b
To find the value of 'b', we can substitute the given values. It states that 1.5 inches have already accumulated after a certain number of hours. Therefore, we can substitute 'x' with the number of hours (let's call it 'h') and 'y' with the corresponding amount of rain:
1.5 = 0.5h + b
Now, our equation becomes:
y = 0.5x + 1.5
Next, to find the number of hours required for 5 inches of rain, we need to solve for 'x' when 'y' is equal to 5:
5 = 0.5x + 1.5
Simplifying the equation, we have:
0.5x = 5 - 1.5
0.5x = 3.5
To isolate 'x', we divide both sides of the equation by 0.5:
x = 3.5 / 0.5
x = 7
Therefore, if 5 inches of rain have accumulated, it would take 7 hours for that to happen.
In summary, the linear equation that models the rain accumulated is y = 0.5x + 1.5, and it would take 7 hours for 5 inches of rain to accumulate.