uncle eddie finds that he can travel 7 kilometers on a liter of gasoline. after the tune-up, he only uses 5/7 as much gasoline. how much farther in kilometers, can he now drive in 1 liter of gasoline?

To solve this problem, we start by understanding how much gasoline Uncle Eddie uses after the tune-up.

Initially, he could travel 7 kilometers on 1 liter of gasoline. After the tune-up, he uses \( \frac{5}{7} \) as much gasoline as before.

1. **Calculate the gasoline used after the tune-up**:
   Since he now uses \( \frac{5}{7} \) of the gasoline he used before, the amount of gasoline he now uses to travel 7 kilometers is:
   \[
   \text{New gasoline usage} = \frac{5}{7} \times 1 = \frac{5}{7} \text{ liters}
   \]
   So, now he only needs \( \frac{5}{7} \) liters of gasoline to travel 7 kilometers.

2. **Determine the distance he can travel with 1 liter of gasoline**:
   Since \( \frac{5}{7} \) liters takes him 7 kilometers, we can find out how far he can go with 1 full liter by setting up a proportion:
   \[
   \frac{7 \text{ km}}{\frac{5}{7} \text{ liters}} = \text{Distance in km with 1 liter}
   \]
   Simplifying:
   \[
   \text{Distance} = 7 \times \frac{7}{5} = \frac{49}{5} = 9.8 \text{ kilometers}
   \]

3. **Calculate how much farther he can travel**:
   Originally, he could travel 7 kilometers on 1 liter. Now, he can travel 9.8 kilometers on 1 liter. The additional distance he can now travel is:
   \[
   9.8 \text{ km} - 7 \text{ km} = 2.8 \text{ kilometers}
   \]

So, Uncle Eddie can now travel 2.8 kilometers farther on 1 liter of gasoline after the tune-up.

Would you like further details or have any questions?

Here are some related questions:
1. What is the distance Uncle Eddie could travel on 2 liters of gasoline after the tune-up?
2. How would the distance change if the gasoline efficiency improved by \( \frac{4}{5} \) instead of \( \frac{5}{7} \)?
3. If Uncle Eddie's car now consumes 0.1 liters per kilometer, how much gasoline would he need to travel 50 kilometers?
4. What was the original gasoline consumption rate in liters per kilometer before the tune-up?
5. How far can he travel if he has only 3 liters of gasoline after the tune-up?

**Tip**: Understanding proportions can help solve problems involving rates, like fuel efficiency or speed.

Discover how much farther Uncle Eddie can drive on 1 liter of gasoline after his car tune-up. Solve the problem step-by-step using proportions and fuel efficiency concepts. Suitable for Grades 6-8.

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