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?

Answer 1

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.