Working alone and at a constant rate, Machine A takes 3 hours to create a widget. Machine B, working alone and at a constant rate, takes x hours to create a widget. Working together, Machine A and B take 12 hours to build two widgets. What is the value of x?

Time required by Machine B to create a widget = 4 hours

Step-by-step explanation:

Time taken by Machine A ( ) = 3 hours

Time taken by Machine B ( )= x hours

Time taken by both machines by working together = 12 hours

The time required to both machines by  working together to finish a task is given by the formula =

Put the values in above formula we get

⇒ T =  

⇒ 12 =  

⇒ 36 + 12 x = 3 x

⇒ x = - 4 hours

This is the time required by Machine B to create a widget.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

sure i'm up for it

step-by-step explanation: