1. **Problem Statement:** An airplane travels 1400 km in the same time a car travels 560 km. The car's speed is 200 kph less than the airplane's speed. Find the rate of each vehicle. 2. **Step 1: Understand the Problem** - We need to find the speeds (rates) of the airplane and the car. - The airplane travels 1400 km, the car 560 km, both in the same time. - The car's speed is 200 kph less than the airplane's speed. 3. **Step 2: Devise a Plan** - Use the formula for time: $$\text{time} = \frac{\text{distance}}{\text{speed}}$$ - Let the airplane's speed be $x$ kph. - Then the car's speed is $x - 200$ kph. - Since time is the same for both, set their times equal: $$\frac{1400}{x} = \frac{560}{x - 200}$$ 4. **Step 3: Carry Out the Plan** - Cross multiply: $$1400(x - 200) = 560x$$ - Expand: $$1400x - 280000 = 560x$$ - Bring terms to one side: $$1400x - 560x = 280000$$ $$840x = 280000$$ - Solve for $x$: $$x = \frac{280000}{840} = 333.33$$ - So, airplane speed $= 333.33$ kph. - Car speed $= 333.33 - 200 = 133.33$ kph. 5. **Step 4: Look Back and Reflect** - Check times: - Airplane time: $$\frac{1400}{333.33} \approx 4.2 \text{ hours}$$ - Car time: $$\frac{560}{133.33} \approx 4.2 \text{ hours}$$ - Times match, solution is consistent. **Final Answer:** - Airplane speed is approximately $333.33$ kph. - Car speed is approximately $133.33$ kph.