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?

Answer 1

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.