Painter takes 2 days to paint a room(4 walls&ceiling). If he works at the same pace, how many days will it take him to paint a room that is twice

Question

as wide, twice as long, and twice as high?

 

Please explain in 7th grade terms.

Answer 1

The surface area of the room is :

 

   4 x length x width <---- 4 walls

  + height x length <--  ceiling

 

If the dimensions are doubled, the surface area becomes:

 

   4  x ( 2 x length x 2 x width) + (2 x height  x 2 x length) =

  16 x length x width + 4 x height x length =

 

 4 ( 4 x length x width + height x length)

 

 which is 4 times the original surface area

 

so it will take the painter 4 times as long or 8 days