Mavis decided to tile the living room using marble tiles.
The dimensions of the tiles are given below:
| Tile type | Length | Width |
| ----------- | --------- | -------- |
| Rectangular | 900 mm | 0.5 m |
| Square | 0.5 m | 0.5 m |
Use the table above to answer the questions that follow.
4.3.1 Mavis claims that she will need a minimum of 30 rectangular tiles to tile the living room only. Verify, showing ALL calculations, whether her statement is valid.
4.3.2 It takes tilers 45 minutes to lay 15 tiles and 25 minutes to grout the whole living room. Mavis claims that the tilers will finish tiling the living room at 9:28 if they started at 8:15 in the morning. Verify, showing ALL calculations, whether her statement is valid.
Answer (1)
Calculate the area of one rectangular tile: A re a = 0.9 m × 0.5 m = 0.45 m 2 . Total area covered by 30 tiles: 13.5 m 2 .
Determine that without the living room's area, verifying Mavis's claim about needing a minimum of 30 tiles is impossible.
Calculate the time to lay one tile: T im e p er t i l e = 3 min u t es / t i l e . If 16 tiles are needed, the tiling will be finished at 9:28.
Conclude that without knowing the number of tiles needed or the living room's area, verifying Mavis's claim about finishing at 9:28 is impossible.
Explanation
Problem Analysis Let's analyze the problem. We are given the dimensions of a rectangular tile and some information about the tiling process. We need to verify two claims made by Mavis. First, whether 30 rectangular tiles are sufficient to tile the living room. Second, whether the tiling will be completed by 9:28 if starting at 8:15.
Area Calculation for Rectangular Tiles
First, let's consider the dimensions of the rectangular tile. The length is 900 mm, which is equal to 0.9 meters, and the width is 0.5 meters. The area of one rectangular tile is: A re a = l e n g t h × w i d t h = 0.9 m × 0.5 m = 0.45 m 2 If Mavis uses 30 rectangular tiles, the total area covered by these tiles is: T o t a l A re a = 30 × 0.45 m 2 = 13.5 m 2 Without knowing the area of the living room, we cannot verify if 30 tiles are sufficient. We can only say that 30 tiles will cover an area of 13.5 m 2 .
Time Calculation for Tiling and Grouting
Now, let's analyze the second claim. It takes 45 minutes to lay 15 tiles. So, the time to lay one tile is: T im e p er t i l e = 15 t i l es 45 min u t es = 3 min u t es / t i l e The total number of tiles needed is unknown. Let's assume Mavis needs 'N' tiles to tile the living room. The total time to lay N tiles is: L a y in g t im e = N × 3 min u t es The total time for tiling and grouting is: T o t a l t im e = L a y in g t im e + 25 min u t es = 3 N + 25 min u t es The tilers start at 8:15. The end time is: E n d t im e = St a r t t im e + T o t a l t im e = 8 : 15 + ( 3 N + 25 ) min u t es We can rewrite 8:15 as 8 hours and 15 minutes, which is 8 × 60 + 15 = 495 minutes from midnight. So, E n d t im e = 495 + 3 N + 25 = 520 + 3 N min u t es f ro m mi d ni g h t Mavis claims that the tilers will finish at 9:28, which is 9 hours and 28 minutes, or 9 × 60 + 28 = 568 minutes from midnight. So, we need to check if: 520 + 3 N = 568 3 N = 568 − 520 = 48 N = 3 48 = 16 If Mavis needs 16 tiles, the tiling will be finished at 9:28. However, we don't know the actual number of tiles needed. Therefore, we cannot verify Mavis's claim without knowing the area of the living room or the number of tiles needed.
Final Conclusion
In conclusion, we cannot verify either of Mavis's claims without knowing the area of the living room or the number of tiles needed. For the first claim, we can only state that 30 rectangular tiles will cover an area of 13.5 m 2 . For the second claim, if Mavis needs 16 tiles, the tiling will be finished at 9:28.
Examples
When planning home renovations, calculating the area covered by tiles and the time required for installation is crucial. For example, if you're tiling a bathroom floor, knowing the tile dimensions helps determine how many tiles you need. Similarly, understanding the installation rate allows you to estimate the project's duration, aiding in scheduling and budgeting.
