Ajogger ran 2 miles, decreased her speed by 1 mile per hour, and then ran another 3 miles. if her total jogging time was 11/14 hours, find her speed for each part of her run

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.