A cannery processed 1,445 pounds of strawberries in 4.5 hours. The cannery processed 2,320 pounds in 8 hours. Write a linear equation to model the relationship between the weight of strawberries S and time T. How many pounds of strawberries can be processed in 11 hours?
To write a linear equation to model the relationship between the weight of strawberries S and time T, we can use the formula for finding the slope of a line:
Slope (m) = (change in y)/(change in x)
In this case, the change in weight (y) is 2,320 pounds - 1,445 pounds = 875 pounds, and the change in time (x) is 8 hours - 4.5 hours = 3.5 hours.
So, the slope is:
m = 875 pounds / 3.5 hours = 250 pounds per hour
Now we can use the slope-intercept form of a linear equation, y = mx + b, and plug in the values of the slope (m) and one point's coordinates (x, y) to find the y-intercept (b).
Let's use the point (4.5, 1,445):
1,445 pounds = 250 pounds per hour * 4.5 hours + b
1,445 pounds = 1,125 pounds + b
b = 320 pounds
Therefore, the equation that models the relationship between the weight of strawberries S and time T is:
S = 250T + 320
To find the number of pounds of strawberries that can be processed in 11 hours, we can plug in T = 11 into the equation:
S = 250 * 11 + 320
S = 2,770 + 320
S = 3,090 pounds
Therefore, 3,090 pounds of strawberries can be processed in 11 hours.
To write a linear equation to model the relationship between the weight of strawberries S and time T, we first need to find the rate at which strawberries are processed. This can be calculated by dividing the change in weight of strawberries by the change in time.
The change in weight is 2,320 pounds - 1,445 pounds = 875 pounds.
The change in time is 8 hours - 4.5 hours = 3.5 hours.
The rate at which strawberries are processed is given by:
rate = change in weight / change in time
rate = 875 pounds / 3.5 hours
rate = 250 pounds per hour
Now that we have the rate, we can write the linear equation. In a linear equation, the weight of strawberries (S) is equal to the rate (250 pounds per hour) multiplied by the time (T) plus an initial weight (b). The initial weight represents the weight of strawberries at the beginning.
Therefore, the linear equation is:
S = 250T + b
To find the initial weight (b), we can use one of the given data points. Let's use the first data point: 1,445 pounds in 4.5 hours.
Substituting the weight (S) and time (T) values into the equation, we have:
1,445 = 250 * 4.5 + b
1,445 = 1,125 + b
Simplifying the equation, we find:
b = 1,445 - 1,125 = 320 pounds
Now we can rewrite the linear equation with the value of b:
S = 250T + 320
To find how many pounds of strawberries can be processed in 11 hours, we substitute T = 11 into our equation:
S = 250 * 11 + 320
S = 2,750 + 320
S = 3,070 pounds
Therefore, in 11 hours, the cannery can process 3,070 pounds of strawberries.
To write a linear equation to model the relationship between the weight of strawberries S and time T, we can use the slope-intercept form of a linear equation: y = mx + b.
Let's let S represent the weight of strawberries and T represent the time in hours.
We have two data points that we can use to find the equation:
(1) When T = 4.5 hours, S = 1445 pounds
(2) When T = 8 hours, S = 2320 pounds
To find the slope, m, we can use the formula: m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
Using points (4.5, 1445) and (8, 2320), we can now find the slope:
m = (2320 - 1445) / (8 - 4.5) = 875 / 3.5 = 250
Now, we can substitute one of the points (x1, y1) into the slope-intercept form and solve for b:
1445 = 250(4.5) + b
1445 = 1125 + b
b = 1445 - 1125
b = 320
The equation that models the relationship between the weight of strawberries S and time T is therefore:
S = 250T + 320
To find how many pounds of strawberries can be processed in 11 hours, we substitute T = 11 into the equation:
S = 250(11) + 320
S = 2750 + 320
S = 3070
Therefore, in 11 hours, the cannery can process 3070 pounds of strawberries.