Question

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.

Answer 1

Hello!

The answer is:

It will take 7.5 hours to paint the room together.

Why?

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:

`(1Room)/(12hours)*t=(t)/(12)`

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:

`(1Room)/(20hours)*t=(t)/(20)`

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

`(t)/(12)+(t)/(20)=1\\\\(12*t+20*t)/(12*20)=1\\\\(12t+20t)/(240)=1\\\\(32t)/(240)=1\\\\32t=240*1\\\\t=(240)/(32)=7.5`

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

Have a nice day!