Vikas can cover a distance of `20 2/3` — km in `7 3/4` hours on foot. How many km per hour does he walk?

Answer

To find out how many kilometers per hour Vikas walks, we need to divide the total distance he covers by the total time he takes. Here’s the step-by-step solution:

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

1. **Convert `20 2/3` km:**
- Multiply the whole number (20) by the denominator (3): \(20 \times 3 = 60\)
- Add the numerator (2): \(60 + 2 = 62\)
- So, \(20 2/3 = \frac{62}{3}\) km.

2. **Convert `7 3/4` hours:**
- Multiply the whole number (7) by the denominator (4): \(7 \times 4 = 28\)
- Add the numerator (3): \(28 + 3 = 31\)
- So, \(7 3/4 = \frac{31}{4}\) hours.

### Step 2: Set Up the Division
Now, we need to find the speed in km per hour by dividing the distance by the time:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{\frac{62}{3}}{\frac{31}{4}} \]

### Step 3: Divide the Fractions
To divide fractions, we multiply by the reciprocal of the divisor:
\[ \frac{62}{3} \div \frac{31}{4} = \frac{62}{3} \times \frac{4}{31} \]

### Step 4: Simplify the Expression
Now, we can simplify:
- Multiply the numerators: \(62 \times 4 = 248\)
- Multiply the denominators: \(3 \times 31 = 93\)

So we have:
\[ \frac{248}{93} \]

### Step 5: Convert to Mixed Number (if needed)
Now, we can convert \(\frac{248}{93}\) to a mixed number:
- Divide 248 by 93, which goes 2 times (since \(93 \times 2 = 186\)).
- The remainder is \(248 - 186 = 62\).
- So, \(\frac{248}{93} = 2 \frac{62}{93}\).

### Final Answer
Vikas walks approximately \(2 \frac{62}{93}\) km per hour.

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