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?
Let x = Payton's speed, then 1.5x = Angie's
2.5(x+1.5x) = 20
Solve for x, then 1.5x.
To find out how fast each person can jog, we can set up a system of equations using the given information.
Let's say that Payton's jogging speed is x miles per hour. Since Angie jogs 1.5 miles per hour faster than Payton, her speed is x + 1.5 miles per hour.
We know that the distance they have traveled after 2.5 hours is 20 miles.
Payton's distance = Payton's speed × time = x miles per hour × 2.5 hours = 2.5x miles
Angie's distance = Angie's speed × time = (x + 1.5) miles per hour × 2.5 hours = 2.5(x + 1.5) miles
According to the given information, their total distance is 20 miles. So we can set up the equation:
Payton's distance + Angie's distance = 20 miles
2.5x + 2.5(x + 1.5) = 20
Simplifying the equation:
2.5x + 2.5x + 3.75 = 20
5x + 3.75 = 20
5x = 16.25
x = 3.25
So, Payton can jog at a speed of 3.25 miles per hour. Since Angie jogs 1.5 miles per hour faster than Payton, her speed is 3.25 + 1.5 = 4.75 miles per hour.
Therefore, Payton can jog at a speed of 3.25 miles per hour and Angie can jog at a speed of 4.75 miles per hour.