A car is moving at an average speed of `56(3)/(5)`km per hour . How much distance will cover in `7(1)/(2)`hours ?

Answer

To solve the problem of how much distance a car will cover when moving at an average speed of \(56 \frac{3}{5}\) km per hour for \(7 \frac{1}{2}\) hours, we can follow these steps:

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

1. **Convert the speed**:
\[ 56 \frac{3}{5} = \frac{56 \times 5 + 3}{5} = \frac{280 + 3}{5} = \frac{283}{5} \text{ km per hour} \]

2. **Convert the time**:
\[ 7 \frac{1}{2} = \frac{7 \times 2 + 1}{2} = \frac{14 + 1}{2} = \frac{15}{2} \text{ hours} \]

### Step 2: Use the formula to calculate distance

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

Substituting the values we found:
\[ \text{Distance} = \frac{283}{5} \times \frac{15}{2} \]

### Step 3: Simplify the multiplication

1. Multiply the numerators:
\[ 283 \times 15 = 4245 \]

2. Multiply the denominators:
\[ 5 \times 2 = 10 \]

3. So, we have:
\[ \text{Distance} = \frac{4245}{10} \]

### Step 4: Convert to a mixed number

To convert \(\frac{4245}{10}\) to a mixed number:
1. Divide \(4245\) by \(10\):
- \(4245 \div 10 = 424\) remainder \(5\)

Thus, we can write:
\[ \frac{4245}{10} = 424 \frac{5}{10} = 424 \frac{1}{2} \text{ km} \]

### Final Answer
The distance covered by the car in \(7 \frac{1}{2}\) hours is \(424 \frac{1}{2}\) km.

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