To solve this problem, I need to compare the time it will take for Abiana to reach the opposite corner of the rectangular park using a scooter and walking, respectively.
First, I need to find out the distance Abiana will need to cover if she goes around the park. To do this, I can use the Pythagorean Theorem, which states that the square of the length of the hypotenuse (in this case, the distance Abiana needs to travel) is equal to the sum of the squares of the lengths of the other two sides.
So, the square of the distance Abiana needs to travel is equal to (3/4)^2 + 1^2 = 25/16, which means the distance itself is the square root of 25/16 miles, or 5/4 miles.
If Abiana takes a scooter, it will take her 8 minutes to travel 1 mile, so it will take her 8 * 5/4 = 10 minutes to travel the distance around the park.
On the other hand, if Abiana walks directly across the grass, it will take her 20 minutes to travel 1 mile, so it will take her 20 * 5/4 = 25 minutes to travel the diagonal distance of the rectangular park.
Therefore, taking the scooter is the faster mode of transportation, as it will take Abiana 10 minutes to travel the distance around the park, whereas she will need 25 minutes to walk directly across.