To find out how much more Nora's car weighs than Ling's car, we need to subtract Ling's weight from Nora's weight.
First, we convert the mixed numbers to improper fractions:
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Nora's car weighs 6 2/3 tons: \[ 6 \frac{2}{3} = \frac{6 \times 3 + 2}{3} = \frac{18 + 2}{3} = \frac{20}{3} \]
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Ling's car weighs 2 1/4 tons: \[ 2 \frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4} \]
Now, we need to subtract these two fractions: \[ \frac{20}{3} - \frac{9}{4} \]
To do this, we need a common denominator. The least common multiple of 3 and 4 is 12.
Next, we convert each fraction to have the denominator of 12:
For \(\frac{20}{3}\): \[ \frac{20}{3} = \frac{20 \times 4}{3 \times 4} = \frac{80}{12} \]
For \(\frac{9}{4}\): \[ \frac{9}{4} = \frac{9 \times 3}{4 \times 3} = \frac{27}{12} \]
Now we can subtract: \[ \frac{80}{12} - \frac{27}{12} = \frac{80 - 27}{12} = \frac{53}{12} \]
Finally, we can convert \(\frac{53}{12}\) into a mixed number: \[ \frac{53}{12} = 4 \frac{5}{12} \]
Thus, Nora's car weighs \(4 \frac{5}{12}\) tons more than Ling's car.
The final answer is: \[ \boxed{4 \frac{5}{12}} \text{ tons} \]