Ratio and Proportion

Concept:Speed is inversely proportional to time when distance is constant. The ratio of speeds is the inverse ratio of the times taken.Explanation:The distance covered by both the car and the motorcycle is the same (150 km).Convert the car's time into hours: 2 hours and 40 minutes = $2 + \frac{40}{60} = 2 + \frac{2}{3} = \frac{8}{3}$ hours.The motorcycle's time is 2 hours.Since distance is constant, the ratio of speeds (car : motorcycle) equals the inverse ratio of their times.Thus, speed ratio = $\frac{1}{\frac{8}{3}} : \frac{1}{2} = \frac{3}{8} : \frac{1}{2}$.To simplify, multiply both terms by 8: $3 : 4$.Therefore, the car's speed is to the motorcycle's speed as 3 is to 4.Answer:3 : 4