A painter needs 3 days to paint the walls of a room. How long would it take him, working at the same rate, to paint a room that is twice as long, twice as wide and twice as high as the original room?
we are looking at the surface area.
so each wall is four times as large as before. (eg. if one wall is lw, then the corresponding new wall is (2l)(2w) or 4lw)
So it would take him 12 days
(BTW, I could paint that room in 3 hours).
To determine how long it would take for the painter to paint a room that is twice as long, wide, and high as the original room, we can break down the problem and analyze the different dimensions separately.
Let's consider the relationship between the areas of the two rooms. The area of the original room can be calculated by multiplying its length, width, and height:
Area of the original room = Length × Width × Height
Since the new room is twice as long, wide, and high as the original room, its dimensions can be expressed as:
Length of new room = 2 × Length of original room
Width of new room = 2 × Width of original room
Height of new room = 2 × Height of original room
Now, let's calculate the new room's area:
Area of new room = (2 × Length of original room) × (2 × Width of original room) × (2 × Height of original room)
= (2 × 2 × 2) × (Length of original room × Width of original room × Height of original room)
= 8 × (Area of original room)
So, the new room has an area that is 8 times greater than the original room.
Now, let's relate the time it takes to paint the two rooms. The area of the room represents the amount of work the painter needs to complete. Assuming the painter works at the same rate, we can conclude that the time it takes to paint the room is directly proportional to its area.
Therefore, if the new room has an area that is 8 times greater than the original room, the time it will take to paint the new room will also be 8 times longer.
Since the painter takes 3 days to paint the original room, it will take him:
Time to paint new room = 8 × (Time to paint original room)
= 8 × 3 days
= 24 days
So, it would take the painter 24 days to paint a room that is twice as long, wide, and high as the original room, assuming he works at the same rate.