1. **State the problem:** An engineer drives to his brother's house at 50 mph taking 3 hours. We need to find the time it takes to drive back at 60 mph. 2. **Calculate the distance to the brother's house:** $$\text{Distance} = \text{Speed} \times \text{Time} = 50 \times 3 = 150 \text{ miles}$$ 3. **Calculate the time to drive home:** Using the same distance, time is distance divided by speed: $$\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{150}{60} = 2.5 \text{ hours}$$ 4. **Final answer:** It takes him 2.5 hours to drive home.