Colleen can paint a room in 12 hours. rebecca can paint the same room in 20 hours. how long does it take for both colleen and rebecca to paint the room if they are working together? write an equation that using the variable t to represent the time it takes to paint the room together that can be used to solve the problem.

The answer is:

It will take 7.5 hours to paint the room together.

Using the given information we need to write an equation considering both Colleen and Rebecca rates.

For Colleen we know that she can paint a room in 12 hours, so, her equation will be:

Being "t" the time used to paint.

For Rebecca, we know that she can paint a room in 20 hours, so, her equation will be:

Now, if we want to calculate the time needed to paint 1 room, we have:

Hence, we have that it will take 7.5 hours to paint the room together.

Have a nice day!

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

range is infinite on both x and y axis positive and negative

step-by-step explanation: