Question: 2. Driving Distance
Carlos drove 4¾ kilometers to the store. He then drove another 2⅓ kilometers to the park. On the way back, he took a shortcut that was ¾ of the total distance he had driven so far. How far did he drive on the shortcut?
1. **State the problem:** Carlos drives 4\frac{3}{4} kilometers to the store, then 2\frac{1}{3} kilometers to the park. He takes a shortcut back that is \frac{3}{4} of the total distance driven so far. We need to find the length of the shortcut.
2. **Convert mixed numbers to improper fractions:**
\[4\frac{3}{4} = \frac{19}{4}, \quad 2\frac{1}{3} = \frac{7}{3}\]
3. **Calculate total distance before shortcut:**
\[\text{Total distance} = \frac{19}{4} + \frac{7}{3} = \frac{19 \times 3}{4 \times 3} + \frac{7 \times 4}{3 \times 4} = \frac{57}{12} + \frac{28}{12} = \frac{85}{12}\]
4. **Calculate shortcut distance:**
\[\text{Shortcut} = \frac{3}{4} \times \frac{85}{12} = \frac{3 \times 85}{4 \times 12} = \frac{255}{48}\]
5. **Simplify the fraction:**
\[\frac{255}{48} = \frac{\cancel{15} \times 17}{\cancel{15} \times 3.2} \text{ but since 15 does not divide 48 exactly, simplify by 3:}\]
\[\frac{255}{48} = \frac{85}{16} = 5\frac{5}{16}\]
6. **Final answer:** Carlos drove \boxed{5\frac{5}{16}} kilometers on the shortcut.