A bus is moving at an average speed of `46(2)/(3)Km//h`. How much distance will `2(2)/(5)` hours?

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Convert the mixed fraction speed into an improper fraction.
The average speed given is \(46 \frac{2}{3} \text{ km/h}\).

To convert this into an improper fraction:
1. Multiply the whole number (46) by the denominator (3).
2. Add the numerator (2) to this product.
3. Place this sum over the original denominator (3).

Calculating:
\[ 46 \times 3 = 138 \]
\[ 138 + 2 = 140 \]
Thus, the speed in improper fraction form is:
\[ \frac{140}{3} \text{ km/h} \]

### Step 2: Convert the mixed fraction time into an improper fraction.
The time given is \(2 \frac{2}{5} \text{ hours}\).

To convert this into an improper fraction:
1. Multiply the whole number (2) by the denominator (5).
2. Add the numerator (2) to this product.
3. Place this sum over the original denominator (5).

Calculating:
\[ 2 \times 5 = 10 \]
\[ 10 + 2 = 12 \]
Thus, the time in improper fraction form is:
\[ \frac{12}{5} \text{ hours} \]

### Step 3: Use the formula for distance.
The formula for distance is:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

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

### Step 4: Multiply the fractions.
To multiply the fractions, multiply the numerators and the denominators:
\[ \text{Distance} = \frac{140 \times 12}{3 \times 5} = \frac{1680}{15} \]

### Step 5: Simplify the fraction.
Now, we simplify \(\frac{1680}{15}\):
1. Divide both the numerator and the denominator by 15.

Calculating:
\[ 1680 \div 15 = 112 \]
Thus, the distance covered by the bus is:
\[ \text{Distance} = 112 \text{ km} \]

### Final Answer:
The bus will cover a distance of **112 km** in \(2 \frac{2}{5}\) hours.

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