The Eastminster Widget Company has an old machine that can produce 36 widgets in 9 hours, and a newer machine that can produce 40 widgets in 8
hours. Working together, how long would it take to produce 100 widgets?

22 hours

Step-by-step explanation:

Old machine produces 36 widgets in 9 hours. The number of widgets produced in an hour can be determined as;

In 1 hour =

              = 4 widgets

New machine can produce 40 widgets in 8 hours. The umber of widgets produced in an hour can be determined as;

In 1 hour =

              = 5 widgets

Thus, let the time required by old machine be represented by s, and that of new machine by y. Working together we have;

4x + 5y = 100

(4 * 10) + (5 * 12) = 100

Thus the old machine would work for 10 hours, while the new machine would work for 12 hours to produce 100 widgets.

Working together, it would take both machines 22 hours.

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0