A car covers 641 `1/4` km in 43 `1/8` litres of fuel. How much distance can this car cover in 1 litre of fuel?

Answer

To find out how much distance a car can cover in 1 litre of fuel, we need to divide the total distance covered by the total fuel consumed. Let's break down the solution step by step.

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

1. **Convert 641 `1/4` km:**
- Multiply the whole number (641) by the denominator (4):
\( 641 \times 4 = 2564 \)
- Add the numerator (1):
\( 2564 + 1 = 2565 \)
- So, \( 641 \frac{1}{4} = \frac{2565}{4} \) km.

2. **Convert 43 `1/8` litres:**
- Multiply the whole number (43) by the denominator (8):
\( 43 \times 8 = 344 \)
- Add the numerator (1):
\( 344 + 1 = 345 \)
- So, \( 43 \frac{1}{8} = \frac{345}{8} \) litres.

### Step 2: Set Up the Division
Now we need to find out how much distance the car can cover in 1 litre of fuel by dividing the total distance by the total fuel.

\[ \text{Distance per litre} = \frac{\text{Total Distance}}{\text{Total Fuel}} = \frac{\frac{2565}{4}}{\frac{345}{8}} \]

### Step 3: Simplify the Division of Fractions
To divide fractions, we multiply by the reciprocal of the divisor.

\[ \frac{2565}{4} \div \frac{345}{8} = \frac{2565}{4} \times \frac{8}{345} \]

### Step 4: Multiply the Fractions
Now, we can multiply the fractions:

\[ = \frac{2565 \times 8}{4 \times 345} \]

### Step 5: Simplify the Expression
Before multiplying, we can simplify:

1. \( 4 \) goes into \( 8 \) two times:
\[ = \frac{2565 \times 2}{345} \]

2. Now calculate \( 2565 \times 2 = 5130 \):
\[ = \frac{5130}{345} \]

### Step 6: Perform the Division
Now we divide \( 5130 \) by \( 345 \):

1. Performing the division:
\[ 5130 \div 345 = 14.86956521739 \approx 14 \frac{20}{23} \text{ km} \]

### Final Answer
Thus, the car can cover approximately \( 14 \frac{20}{23} \) km in 1 litre of fuel.

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