The number of miles per gallon of gasoline that her old car gets is :

\(24:\left(100\%+50\%\right)=16\)

The number of gallons of gasoline that her new car spend to travel 480 miles is : 480 : 24 = 20 

The number of gallons of gasoline that her old car spend to travel 480 miles is : 480 : 16 = 30 

The answer is : 30 - 20 = 10 (gallons of gasoline)