Final answer:
Jimmy will take approximately 1.775 hours to get home.
Step-by-step explanation:
To find out how long it will take Jimmy to get home, we can use the concept of average speed. Average speed is calculated by dividing the total distance traveled by the time taken. In this case, we have the distance and time for two different points. After 3 hours of driving, Jimmy is 740 km from home, and after 6 hours, he is 461 km from home.
We can calculate the average speed for each segment using the formula:
Average Speed = Distance / Time
For the first segment from home to 740 km, the average speed is:
Average Speed = 740 km / 3 hours = 246.67 km/h
For the second segment from 740 km to 461 km, the average speed is:
Average Speed = (740 km - 461 km) / (6 hours - 3 hours) = 259.67 km/h
Since Jimmy is driving at a constant speed, we can assume that his average speed for the entire trip will be the same. Therefore, we can find the time it will take for him to get home by rearranging the average speed formula:
Time = Distance / Average Speed
Using the average speed from the second segment (259.67 km/h), we can calculate the time it will take Jimmy to get home:
Time = 461 km / 259.67 km/h = 1.775 hours.
Therefore, it will take Jimmy approximately 1.775 hours to get home.