Revenue must be greater than Cost: R(x) > C(x), which translates to 0.50x > 10 + 0.20x. After simplification: 0.50x - 0.20x > 10, leading to 0.30x > 10. Therefore, x > 10/0.30 which gives x > 33.333. Rounding up, we find x = 34, meaning at least 34 cups of lemonade must be sold for revenue R(x) to exceed cost C(x). The answer is 34.
Let Leo's speed be denoted as x miles per hour
therefore, Ethan's speed is (x + 6) miles per hour
Applying the formula Distance = Speed × Time
thus the distance Leo covers in 2 hours = x × 2 = 2x
and the distance that Ethan travels in 1.5 hours is 1.5( x + 6 ) = 1.5x + 9
given that they met on the route, after Ethan had cycled for 1.5 hours and Leo for 2 hours, together they covered the entire route measuring 65 miles.
⇒ distance traveled by Leo in 2 hours plus distance traveled by Ethan in 1.5 hours equals 65
⇒ 2x + 1.5x + 9 = 65
⇒ 3.5x = 56
⇒ x = 16
Therefore, Leo's speed is x miles/hr = 16 miles/hour
and Ethan's speed is (x + 6) miles/hr = 16 + 6 = 22 miles/hour
