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 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 and the time it takes to process them, we need to find the rate of processing.
First, we find the rate of processing for 4.5 hours:
rate = weight / time
rate = 1445 pounds / 4.5 hours
rate = 321.11 pounds per hour
Similarly, for 8 hours:
rate = weight / time
rate = 2320 pounds / 8 hours
rate = 290 pounds per hour
Now, we can use the slope-intercept form of a linear equation to find the equation to model the relationship:
y = mx + b
where y represents the weight of strawberries (S), x represents the time in hours (T), m represents the slope (rate of processing), and b represents the y-intercept (starting weight).
Using the rate we found for 4.5 hours (321.11 pounds per hour) and the corresponding weight (1445 pounds), we can find the y-intercept:
1445 = (321.11)(4.5) + b
1445 = 1444.995 + b
b = 0.005
So the equation to model the relationship is:
S = 321.11T + 0.005
Now we can find how many pounds of strawberries can be processed in 11 hours:
S = 321.11(11) + 0.005
S = 3532.11 + 0.005
S = 3532.115
Therefore, approximately 3532.115 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 the time, T, we need to determine the rate at which strawberries are processed.
Let's calculate the rate of strawberry processing for the given data:
Rate = Weight / Time
For the first scenario: 1,445 pounds in 4.5 hours
Rate1 = 1445 / 4.5 = 321.11 pounds per hour
For the second scenario: 2,320 pounds in 8 hours
Rate2 = 2320 / 8 = 290 pounds per hour
Now, let's use the slope-intercept form of a linear equation (y = mx + b) to model the relationship:
S = mT + b
We have two points (T, S) that lie on the line: (4.5, 1445) and (8, 2320). We can use these points to find the slope, m, and the y-intercept, b.
m = (S2 - S1) / (T2 - T1)
m = (2320 - 1445) / (8 - 4.5)
m = 875 / 3.5
m = 250 pounds per hour
Now we can substitute the slope and one of the points into the equation to find the y-intercept, b.
1445 = 250 * 4.5 + b
1445 = 1125 + b
b = 1445 - 1125
b = 320 pounds
So, the equation to model the relationship between the weight of strawberries, S, and the time, T, is:
S = 250T + 320
To find the number of pounds of strawberries that can be processed in 11 hours, we substitute T = 11 into the equation:
S = 250 * 11 + 320
S = 2750 + 320
S = 3070 pounds
Therefore, in 11 hours, 3,070 pounds of strawberries can be processed.
To write a linear equation that models the relationship between the weight of strawberries and the time in hours, we need to find the rate at which the strawberries are processed.
Let's start by finding the rate (R) at which the strawberries are processed. The rate is calculated by dividing the weight of strawberries (S) by the time in hours (T), so we have:
R = S / T
Now, let's find the rate for the two given data points:
- For the first data point: S = 1,445 pounds and T = 4.5 hours
R1 = 1,445 / 4.5 = 321.11 (approximately)
- For the second data point: S = 2,320 pounds and T = 8 hours
R2 = 2,320 / 8 = 290
Since we want to model the relationship between the weight of strawberries (S) and the time in hours (T), the linear equation can be written as:
S = R * T
Using the rate calculated from the second data point (R2 = 290), the equation becomes:
S = 290T
Finally, to find how many pounds of strawberries can be processed in 11 hours, we substitute 11 for T in the equation:
S = 290 * 11 = 3,190 pounds
Therefore, approximately 3,190 pounds of strawberries can be processed in 11 hours.