a jogger 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.