Subjects algebra

Distance Shorter

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1. **Problem statement:** Ramon usually drives $\frac{3}{5}$ of a kilometer to pick up Joe, then they drive another $\frac{4}{5}$ of a kilometer to work. Today, Ramon drives directly to work, which is 1 kilometer. We need to find how much shorter the direct route is compared to the usual route. 2. **Formula and explanation:** The total usual distance is the sum of the two parts: $$\text{Usual distance} = \frac{3}{5} + \frac{4}{5}$$ The direct distance today is 1 kilometer. 3. **Calculate the usual distance:** $$\frac{3}{5} + \frac{4}{5} = \frac{3+4}{5} = \frac{7}{5} = 1.4$$ kilometers. 4. **Calculate how much shorter the direct route is:** $$\text{Difference} = \text{Usual distance} - \text{Direct distance} = 1.4 - 1 = 0.4$$ kilometers. 5. **Answer:** The direct route is $0.4$ kilometers shorter than the usual route.