a couple of days

 girls always f//k up decorating - they prefer chatting and texting

Let area to be painted be A m²

Rate for AJ = A/3 m²/h   = 2A/6 m²/h

Rate for Brianna   = A/2 m²/h   = 3A/6 m²/h

Combined rate   =  5A / 6 m²/h

Time   = A / ( 5A / 6 ) h   = 6/5 h   = 1 h 12 min

2 or 3 days because brothers and sisters fight a lot. - a knowledgeable father. {Just make them responsible for painting their own rooms.} Or, figure AJ does 1/180th of the room per minute while B does 1/120 per minute. Together = 5/360th of the room is finished every minute, then go for the 100%  done (360/5) = 72 minutes aka 1.2 hr.

AJ paints 1/3 of room in 1 hour

Brianna paints 1/2 room in 1 hour

Together, they paint 1/3 + 1/2 of the room in 1 hour

= 2/6 + 3/3

= 5/6 room in 1 hour

= 1/6 room in 60/5 = 12 minutes.

t = 12 x 6 minutes

t = 72 minutes = 1 hour 12 munutes

My son AJ can paint a room in 3 hours. 

My daughter Brianna can paint 

the same room in 2 hours. 

Working together, 

how long would it take them 

to paint the same room? 

Let t = how long it will take them painting together.

1/3 + 1/2 = 1/t

2t + 3t = 6

5t = 6

t = 1.2 hours 

The typical way to solve these problems is to express each as a rate.

AJ can paint 1/3 of a room per hour

Brianna can paint 1/2 of a room per hour.

Add those together:

1/3 + 1/2

= 2/6 + 3/6

= 5/6

So together they can paint 5/6 of a room per hour. Inverting that we see that it will take 6/5 of an hour to paint 1 room.

5/6 room/hour * 6/5 hours = 1 room

6/5 hours = 1.2 hours

0.2 hours * 60 minutes = 12 minutes

Answer:

1 hour and 12 minutes

Now that you've seen the long way using rates, here's a quick shortcut formula.

If the first person takes A units of time and the second takes B units of time, together they will take:

AB / (A + B)

In your case:

A = 3 hours

B = 2 hours

Together = (3*2) / (3+2)

= 6/5 hours

= 1.2 hours (or 1 hour 12 minutes)

AJ can paint 2 rooms in 6 hours.

Brianna can paint 3 rooms in 6 hours

Together AJ and Brianna can paint 5 rooms in 6 hours.

So, together AJ and Brianna can paint a room in  ⁶∕₅ of an hour, which is 1 hour and 12 minutes.

Son = 1 room / 3 hours

Dau = 1 room / 2 hours

Son + Dau = 0.833 room / hour = 1 room / 1.2 hours

AJ paints 1/3 of the room each hour

Brianna paints 1/2 of the room each hour

Together, they paint 1/2 + 1/3 of the room each hour

1/2 + 1/3 =>

3/6 + 2/6 =>

5/6

1 room / (5/6 room/hour) =>

6/5 hours =>

1.2 hours =>

1 hour 12 minutes

Less than 2 hours

1/3 * t + 1/2 * t = 1

solve for t, that is the number of hours.