When rounding to two decimal places, we consider the third decimal place to determine how to round. Since Helen rounded the distance to 1.64 miles, the actual distance must be within the range of 1.635 miles to 1.645 miles (1.635 rounded to 1.64 and 1.645 rounded down to 1.64).
Now, let's evaluate the given options:
A. 1.645 miles - This is at the top of the rounding range and rounds to 1.64. B. 1.633 miles - This is below the rounding range and would round to 1.63. C. 1.642 miles - This is within the rounding range and rounds to 1.64. D. 1.647 miles - This is above the rounding range and would round to 1.65.
From this analysis, the actual distances that could round to 1.64 are 1.645 miles and 1.642 miles.
The correct answers are: A. 1.645 miles and C. 1.642 miles.