The answer & explanation for this question is given in the attachment below.
If you find the discriminant it will tell you the number and types of roots. The discriminant is the value b^2 -4ac.
a = 1
b = 1
c = 1
1^2 - 4*1*1
1-4 = -3
Since this is a negative number there will be 2 complex roots.
Monday: 3 1/4 miles
Tuesday: (3 1/4)(2/3) = 2 1/6 miles
Wednesday: (2 1/6)(2) = 4 1/3 miles
Thursday: (4 1/3)(3/4) = 3 1/4 miles
Add them all up: 13 miles
She has not reached her goal, she needs to ride her bike 2 more miles to reach her goal.
The square root of 169 is 13 and 170 is 13.03