Ethan and Leo start riding their bikes at the opposite ends of a 65-mile bike path. After Ethan has ridden 1.5 hours and Leo has ridden 2 hours, they meet on the path. Ethan's speed is 6 miles per hour faster than Leo's speed. Find the speed of the two bikers

let Leo's speed = x mile/hr

so Ethan speed = (x + 6) miles per hour

Distance = Speed * Time

so distance traveled by Leo in 2 hours = x * 2 = 2x

and distance traveled by Ethan in 1.5 hours = 1.5 (x + 6) = 1.5x + 9

since they meet on the path, After Ethan has ridden 1.5 hours and Leo has ridden 2 hours, so together the have traveled on complete path that is 65 miles.

⇒ distance traveled by leo in 2 hours + distance traveled by Ethan in 1.5 hours = 65

⇒ 2x + 1.5x + 9 = 65

⇒ 3.5x = 56

⇒ x = 16

Hence Leo's speed = x miles/hr = 16 miles/hour

and Ethan's speed = (x + 6) miles/hr = 16 + 6 = 22 mile/hour