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 need to find the rate at which strawberries are processed.
For the first scenario, processing 1,445 pounds of strawberries in 4.5 hours, the rate of processing is:
(1,445 pounds)/(4.5 hours) = 321.11111 pounds/hour (round to 5 decimal places)
For the second scenario, processing 2,320 pounds in 8 hours, the rate of processing is:
(2,320 pounds)/(8 hours) = 290 pounds/hour (rounded to the nearest whole number)
To find the equation, we need the equation of a line in the form of y = mx + b, where y is the weight of strawberries, x is the time, m is the rate of processing, and b is the y-intercept.
Using the rate of processing from the second scenario (290 pounds/hour), we can write the equation as:
S = 290T + b
To find the y-intercept (b), we can use the first scenario. Substituting the weight (1,445 pounds) and time (4.5 hours) into the equation:
1,445 = 290(4.5) + b
1,445 = 1,305 + b
b = 1,445 - 1,305
b = 140
Therefore, the equation to model the relationship between the weight of strawberries S and time T is:
S = 290T + 140
To find the weight of strawberries that can be processed in 11 hours, we can substitute T = 11 into the equation:
S = 290(11) + 140
S = 3,190 + 140
S = 3,330
Therefore, 3,330 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 the rate of processing:
Rate = Weight / Time
Using the information given, we can create two data points to form the equation:
First data point: (4.5 hours, 1,445 pounds)
Second data point: (8 hours, 2,320 pounds)
To find the rate in terms of pounds per hour, we can calculate the difference in weight divided by the difference in time:
Rate = (2,320 pounds - 1,445 pounds) / (8 hours - 4.5 hours)
Rate = 875 pounds / 3.5 hours
Rate = 250 pounds/hour
Using the slope-intercept form of the equation (y = mx + b), we can write the linear equation as follows:
S = 250T + b
To find b (the y-intercept), we can substitute one of the data points:
1,445 pounds = 250 pounds/hour × 4.5 hours + b
1,445 pounds = 1,125 pounds + b
b = 1,445 pounds - 1,125 pounds
b = 320 pounds
Now we can rewrite the linear equation:
S = 250T + 320
To determine how many pounds of strawberries can be processed in 11 hours, we need to substitute T = 11 into the 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, we need to determine the rate at which the cannery processes strawberries. We can do this by finding the ratio of pounds of strawberries to hours.
First, we calculate the rate for the first scenario, where 1,445 pounds of strawberries were processed in 4.5 hours:
Rate = Pounds / Hours
Rate1 = 1,445 pounds / 4.5 hours
Now, we calculate the rate for the second scenario, where 2,320 pounds of strawberries were processed in 8 hours:
Rate2 = 2,320 pounds / 8 hours
These two rates represent the same cannery processing strawberries at different times. We can write a linear equation using this information:
Rate1 = Rate2
1,445 pounds / 4.5 hours = 2,320 pounds / 8 hours
Now, we can solve for the weight of strawberries that can be processed in 1 hour:
1,445 pounds / 4.5 hours = S pounds / 1 hour
Solving for S, we get:
S = (1,445 pounds / 4.5 hours) * 1 hour
S = 1,445 pounds / 4.5
Simplifying the equation, we find that the rate at which the cannery processes strawberries is approximately 321.11 pounds per hour.
To find how many pounds of strawberries can be processed in 11 hours, we can multiply the rate by the number of hours:
Pounds = Rate * Hours
Pounds = 321.11 pounds/hour * 11 hours
Simplifying the equation, we get:
Pounds = 3,532.21 pounds
Therefore, approximately 3,532.21 pounds of strawberries can be processed in 11 hours.