Starting at the same point, Angie and Payton jog in opposite directions. Angie can jog 1.5 miles per hour faster than Payton. After 2.5 hours, they are 20 miles apart. How fast can each person jog?

To solve this problem, we can set up a system of equations using the given information.

Let's assume that Payton's jogging speed is x miles per hour. According to the problem, Angie can jog 1.5 miles per hour faster than Payton, so her jogging speed would be x + 1.5 miles per hour.

We can calculate the distance traveled by each person using the formula: Distance = Speed × Time.

After 2.5 hours, Payton would have traveled a distance of 2.5x miles, and Angie would have traveled a distance of 2.5(x + 1.5) miles.

Since they are moving in opposite directions, the total distance between them is the sum of the distances traveled by each person. According to the problem, this total distance is 20 miles.

Therefore, we have the equation: 2.5x + 2.5(x + 1.5) = 20.

To solve this equation, we can simplify it:

2.5x + 2.5x + 3.75 = 20.

Combining like terms:

5x + 3.75 = 20.

Next, subtract 3.75 from both sides:

5x = 20 - 3.75.

Simplifying:

5x = 16.25.

Finally, divide both sides by 5 to solve for x:

x = 16.25 / 5.

Calculating the result:

x = 3.25.

Therefore, Payton's jogging speed is 3.25 miles per hour.

To find Angie's jogging speed, we add the 1.5 miles per hour faster that she jogs:

x + 1.5 = 3.25 + 1.5 = 4.75.

Therefore, Angie's jogging speed is 4.75 miles per hour.