First, we start the problem with the equation 2/3*x = 24 miles. Next, we need to isolate the variable by dividing both sides of the equation by 2/3. This gives us x = (24 miles) / (2/3) = (24 miles) / (2/3) * (3/2) = (24 miles) * (3/2) miles/day = 72/2 miles/day = 36 days. Answer: \boxed{36}.
