Sally can paint a room in 3 hours while it takes Steve 5 hours to paint the same room. How long would it take them to paint the room if they worked together?

Question

Sally can paint a room in 3 hours while it takes Steve 5 hours to paint the same room. How long would it take them to paint the room if they worked together?

Answer 1

Sally can paint a room in 3 hours, so she can paint 1/3 of a room per hour.  Steve can paint a room in 5 hours, so he can paint 1/5 of a room per hour.  Together, they can paint 1/3 + 1/5 of the room per hour, which equals 8/15 of the room per hour.

At the rate of 8/15 of a room per hour, the two could paint 1 room in 1 ÷ 8/15 = 15/8 hours, or 1.875 hrs.

Answer 2

Each hour, Sally paints 1/3 of the room and Steve paints 1/5 of the room.

 

If it takes both of them x hours to paint the room it they are both working together, then, each hour, 1/x of the room gets painted.

 

So, 1/3 + 1/5 = 1/x

 

Multiply both sides by the LCD, 15x:  5x + 3x = 15

 

                                                           8x = 15

 

                                                             x = 15/8 hours

 

                                                               = 1.875 hours

 

                                                               = 1 hr 52 min 30 sec