Using proportions, it is found that the family will drive 482.8 km on the new route.
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, the family travels a distance of 125% of 240 miles, hence the distance is:
D = 1.25 x 240 = 300 miles.
Since there are are approximately 48.28 kilometers in 30 miles, and 300/30 = 10, the distance in kilometers is given by:
D = 48.28 x 10 = 482.8 km.
More can be learned about proportions at https://brainly.com/question/24372153
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