Final answer:
Leo's speed is 16 mph, and Ethan's speed, who is 6 mph faster, is 22 mph. This is determined by setting up a system of equations based on the given distances and times and solving for Leo's speed first.
Step-by-step explanation:
To find the speed of the bikers Ethan and Leo, who start riding their bikes at opposite ends of a 65-mile path, we can set up a system of equations. If Ethan takes 1.5 hours to meet Leo and is 6 mph faster, while Leo takes 2 hours, we can let x represent Leo's speed and x + 6 will represent Ethan's speed.
Since distance equals speed multiplied by time, Leo's distance can be represented as x × 2 and Ethan's distance as (x + 6) × 1.5. Together, they cover the entire 65-mile path, so the equation is x × 2 + (x + 6) × 1.5 = 65. Solving this equation gives us Leo's speed, and adding 6 to it gives us Ethan's speed.
2x + 1.5x + 9 = 65
3.5x + 9 = 65
3.5x = 56
x = 16
Therefore, Leo's speed is 16 mph, and Ethan's speed is 16 mph + 6 mph = 22 mph.