A car is moving at an average speed of `3 (1)/(9) ` km/h. How much distacne will it cover in `5 (1)/(7)` hours ?

Options

A. 16 km
B. 18 km
C. 14 km
D. 20 km

Answer

To find the distance covered by the car, we can use the formula:

\[ \text{Distance} = \text{Speed} \times \text{Time} \]

### Step 1: Convert the mixed numbers to improper fractions

1. **Convert the speed** \(3 \frac{1}{9}\) km/h to an improper fraction:
\[ 3 \frac{1}{9} = \frac{3 \times 9 + 1}{9} = \frac{27 + 1}{9} = \frac{28}{9} \text{ km/h} \]

2. **Convert the time** \(5 \frac{1}{7}\) hours to an improper fraction:
\[ 5 \frac{1}{7} = \frac{5 \times 7 + 1}{7} = \frac{35 + 1}{7} = \frac{36}{7} \text{ hours} \]

### Step 2: Substitute the values into the distance formula

Now we can substitute the values of speed and time into the distance formula:
\[ \text{Distance} = \frac{28}{9} \times \frac{36}{7} \]

### Step 3: Multiply the fractions

To multiply the fractions, we multiply the numerators and the denominators:
\[ \text{Distance} = \frac{28 \times 36}{9 \times 7} \]

### Step 4: Simplify the multiplication

1. Calculate the numerator:
\[ 28 \times 36 = 1008 \]

2. Calculate the denominator:
\[ 9 \times 7 = 63 \]

So we have:
\[ \text{Distance} = \frac{1008}{63} \]

### Step 5: Simplify the fraction

Now we simplify \(\frac{1008}{63}\):
1. Divide both the numerator and the denominator by 63:
\[ 1008 \div 63 = 16 \]

Thus, the distance covered by the car is:
\[ \text{Distance} = 16 \text{ km} \]

### Final Answer:
The car will cover **16 km** in \(5 \frac{1}{7}\) hours.

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