1. **State the problem:** We are given a rocket traveling to Venus. It took 4 days to reach the moon, traveling 4.8 \times 10^{5} km. We need to: a. Calculate the distance traveled in 12 days, expressing the answer in standard form. b. Given the total distance to Venus is 4.8 \times 10^{7} km, calculate the number of days for the journey. 2. **Formula and rules:** - Speed = Distance / Time - Distance = Speed \times Time - Time = Distance / Speed Since the rocket travels at constant speed, speed is constant. 3. **Step a: Calculate distance in 12 days** - First, find the speed: $$\text{Speed} = \frac{4.8 \times 10^{5} \text{ km}}{4 \text{ days}} = 1.2 \times 10^{5} \text{ km/day}$$ - Then, distance in 12 days: $$\text{Distance} = \text{Speed} \times 12 = 1.2 \times 10^{5} \times 12 = 1.44 \times 10^{6} \text{ km}$$ - Expressed in standard form: $$1.44 \times 10^{6} \text{ km}$$ 4. **Step b: Calculate number of days for total journey** - Total distance to Venus: $$4.8 \times 10^{7} \text{ km}$$ - Using speed from above: $$\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{4.8 \times 10^{7}}{1.2 \times 10^{5}}$$ - Simplify: $$= \frac{4.8}{1.2} \times 10^{7 - 5} = 4 \times 10^{2} = 400 \text{ days}$$ **Final answers:** a. Distance traveled in 12 days is $1.44 \times 10^{6}$ km. b. Number of days for the journey to Venus is 400 days.