Find the distance covered by a car in `2(2/5)` hours at a speed of `46(2/3)` km per hour.

Answer

To find the distance covered by a car in \(2 \frac{2}{5}\) hours at a speed of \(46 \frac{2}{3}\) km per hour, we can follow these steps:

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

1. **Convert \(2 \frac{2}{5}\)**:
\[ 2 \frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{10 + 2}{5} = \frac{12}{5} \]

2. **Convert \(46 \frac{2}{3}\)**:
\[ 46 \frac{2}{3} = \frac{46 \times 3 + 2}{3} = \frac{138 + 2}{3} = \frac{140}{3} \]

### Step 2: Use the formula for distance.

The formula for distance is:
\[ \text{Distance} = \text{Time} \times \text{Speed} \]

Substituting the values we found:
\[ \text{Distance} = \frac{12}{5} \times \frac{140}{3} \]

### Step 3: Multiply the fractions.

To multiply the fractions, multiply the numerators and the denominators:
\[ \text{Distance} = \frac{12 \times 140}{5 \times 3} = \frac{1680}{15} \]

### Step 4: Simplify the fraction.

Now, simplify \(\frac{1680}{15}\):
1. Divide both the numerator and the denominator by 15:
\[ 1680 \div 15 = 112 \]
\[ 15 \div 15 = 1 \]

Thus, the simplified distance is:
\[ \text{Distance} = 112 \text{ km} \]

### Final Answer:
The distance covered by the car is **112 kilometers**.

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