To determine the number of tiles needed for the kitchen floor, we need to calculate the area of the kitchen in square feet and the area of each tile in square feet, then find out how many tiles are required to cover the entire floor.

Step 1: Calculate the Area of the Kitchen

The kitchen is a rectangle with dimensions of 8 feet by 17 feet.

$\text{Area of the kitchen} = \text{length} \times \text{width} = 8 \, \text{feet} \times 17 \, \text{feet} = 136 \, \text{square feet}$

Step 2: Calculate the Area of Each Tile

The tiles are square and measure 6 inches by 6 inches. First, convert the measurements from inches to feet.

$6 \, \text{inches} = \frac{6}{12} \, \text{feet} = 0.5 \, \text{feet}$

So, each tile has dimensions of 0.5 feet by 0.5 feet. The area of each tile is:

$\text{Area of each tile} = 0.5 \, \text{feet} \times 0.5 \, \text{feet} = 0.25 \, \text{square feet}$

Step 3: Calculate the Number of Tiles Needed

To find out how many tiles are required to cover the kitchen floor, divide the total area of the kitchen by the area of one tile.

$\text{Number of tiles} = \frac{\text{Area of the kitchen}}{\text{Area of each tile}} = \frac{136 \, \text{square feet}}{0.25 \, \text{square feet per tile}} = 544$

Therefore, the flooring company will need to buy 544 tiles to re-tile your kitchen.

Would you like more details or have any questions? Here are some additional related questions to explore:

1. How many tiles would be needed if the kitchen dimensions were 10 ft by 15 ft?
2. What is the total cost if each tile costs $2.50?
3. How many extra tiles should be purchased to account for potential breakage?
4. How many tiles would be needed if the tiles were 8 inches by 8 inches?
5. How would the number of tiles change if there were a 1-inch gap between each tile?
6. What is the total perimeter of the kitchen?
7. How many tiles would be required if the kitchen had a different shape, such as an L-shape?
8. What is the total weight of the tiles if each tile weighs 1.5 pounds?

Tip: When working with dimensions and areas, always ensure all units are consistent before performing calculations.