Andrew can paint 2 walls in 6.5 hours. Tim can paint 3 walls in 8 hours. Compare the proportional relationships.
A. Tim paints at a faster rate because he paints one wall in 2 2/3 hours while Andrew paints one wall in 3.25 hours
B. Andrew paints at a faster rate because he paints at a rate of about 0.308 while Tim paints at a rate of 0.375
C. Tim paints at a faster rate because he paints at a rate of 0.375 while Andrew paints at a rate of 3.25
D. Andrew paints at a faster rate because he paints 1 wall in 3.25 hours while Tim paints 1 wall 2 2/3 hours
A. Tim paints at a faster rate because he paints one wall in 2 2/3 hours while Andrew paints one wall in 3.25 hours
To determine which painter is faster, we need to compare their rates. The rate can be calculated by dividing the number of walls painted by the time taken.
Let's start with Andrew:
- Andrew can paint 2 walls in 6.5 hours.
So his rate would be: 2 walls / 6.5 hours = 0.308 walls per hour.
Now let's calculate Tim's rate:
- Tim can paint 3 walls in 8 hours.
So his rate would be: 3 walls / 8 hours = 0.375 walls per hour.
Now we can compare the rates given in the answer choices:
A. The answer states that Tim paints one wall in 2 2/3 hours (about 2.67 hours), which would be a rate of approximately 1/2.67 walls per hour, not 0.375. So this option is incorrect.
B. The answer states that Andrew's rate is about 0.308, which matches the calculated rate for Andrew. However, Tim's rate is incorrectly stated as 0.375 instead of 1/2.67. So this option is also incorrect.
C. The answer states that Tim's rate is 0.375, which matches the calculated rate for Tim. However, Andrew's rate is incorrectly stated as 3.25 instead of 0.308. So this option is incorrect as well.
D. The answer states that Andrew paints 1 wall in 3.25 hours, which matches the calculated rate for Andrew. Tim's rate is correctly stated as 1/2.67. So this option is correct.
Therefore, the correct answer is D. Andrew paints at a faster rate because he paints 1 wall in 3.25 hours while Tim paints 1 wall in 2 2/3 hours.
To compare the proportional relationships between Andrew and Tim, we need to determine the time it takes for each of them to paint one wall.
Andrew can paint 2 walls in 6.5 hours, so he takes 6.5/2 = 3.25 hours to paint one wall.
Tim can paint 3 walls in 8 hours, so he takes 8/3 = 2 2/3 hours to paint one wall.
Comparing the two:
A. Tim paints at a faster rate because he paints one wall in 2 2/3 hours while Andrew paints one wall in 3.25 hours. This statement is true.
B. Andrew paints at a faster rate because he paints at a rate of about 0.308 while Tim paints at a rate of 0.375. This statement is not comparing the time taken for one wall, so it is not a valid comparison.
C. Tim paints at a faster rate because he paints at a rate of 0.375 while Andrew paints at a rate of 3.25. Once again, this statement is not comparing the time taken for one wall, so it is not a valid comparison.
D. Andrew paints at a faster rate because he paints 1 wall in 3.25 hours while Tim paints 1 wall in 2 2/3 hours. This statement is false because Tim takes less time to paint one wall.
Therefore, the correct answer is A. Tim paints at a faster rate because he paints one wall in 2 2/3 hours while Andrew paints one wall in 3.25 hours.