It takes a worker 2 hours to lay tile for a floor space that is in shape of a square which measures 6 ft long on each side. How long will it take this same worker to lay the tiles for a square floor space that measures 15 ft long on each side. Show the work please.
First, find the rate at which the worker can lay tiles. This rate can be found as floor area divided by time. Since the worker can lay tiles for the floor space in a shape of a square with a 6 ft side in 2 hours, his work rate is
36/2 = 18 square feet per hour.
(The area of a square with a side of 6 ft is 36 square ft.)
Then, the area of a square floor space with a side of 15 ft is 15*15= 225 square feet, and the time it would take the worker to lay tiles would be area divided by rate:
225/18 = 25/2=12.5 hours.
It would take the worker 12.5 houra to lay tiles on this floor space.
Since it is a square which measure 6 ft on all sides we know the total area of the square is 36 ft squared. If it takes the worker 120 minutes (2 hours) to completely tile the square floor then we know he is laying tiles at the rate of 120/36 = 3.3 minutes for each foot squared.
The new square floor is 15 ft by 15 ft which is 225 ft squared. If we assume he works at the same rate of 3.3 minutes for each ft squared then we simply multiply 225 ft by 3.3 minutes. 225 x 3.3 = 742.5. This means the worker will take 742.5 minutes or 12.4 hours to completely lay the tiles for a square floor space that measures 15 ft long on each side.