Answer:
7 mph, 6 mph
Step-by-step explanation:
Let's say x is her speed during the first 2 miles, and x−1 is her speed during the last 3 miles.
The time it takes for her to run the first 2 miles is:
t = 2 / x
The time it takes for her to run the last 3 miles is:
t = 3 / (x−1)
The total time is 11/14 hours:
11/14 = 2/x + 3/(x−1)
Multiply both sides by x (x−1).
11/14 x (x−1) = 2(x−1) + 3x
11/14 (x²−x) = 2x − 2 + 3x
11/14 (x²−x) = 5x − 2
Multiply both sides by 14:
11 (x²−x) = 70x − 28
11x² − 11x = 70x − 28
11x² − 81x + 28 = 0
Factor:
(11x − 4) (x − 7) = 0
x = 4/11 or 7
Since x must be greater than 1 (x−1 must be positive), that means x = 7 and x−1 = 6.
Her speed during the first part was 7 mph, and her speed during the second part was 6 mph.
