A car travels 283`1/2` km in 4`2/3` hours. How far does this car go in 1 hour, travelling at the same speed?

Answer

To solve the problem step by step, we need to find out how far the car travels in one hour given that it travels 283 1/2 km in 4 2/3 hours.

### Step 1: Convert mixed numbers to improper fractions
First, we convert the mixed numbers into improper fractions.

- For 283 1/2:
\[ 283 \frac{1}{2} = \frac{2 \times 283 + 1}{2} = \frac{566 + 1}{2} = \frac{567}{2} \]

- For 4 2/3:
\[ 4 \frac{2}{3} = \frac{3 \times 4 + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3} \]

### Step 2: Set up the division
Now, we need to find out how far the car travels in 1 hour. This can be done by dividing the total distance by the total time:
\[ \text{Distance in 1 hour} = \frac{567/2}{14/3} \]

### Step 3: Simplify the division of fractions
To divide by a fraction, we multiply by its reciprocal:
\[ \frac{567}{2} \div \frac{14}{3} = \frac{567}{2} \times \frac{3}{14} \]

### Step 4: Multiply the fractions
Now we multiply the numerators and the denominators:
\[ = \frac{567 \times 3}{2 \times 14} = \frac{1701}{28} \]

### Step 5: Convert the improper fraction back to a mixed number
Now we convert \(\frac{1701}{28}\) back to a mixed number:
1. Divide 1701 by 28:
- 28 goes into 1701 approximately 60 times (since \(28 \times 60 = 1680\)).
- The remainder is \(1701 - 1680 = 21\).

So, we can write:
\[ \frac{1701}{28} = 60 \frac{21}{28} \]

### Final Answer
Thus, the distance traveled by the car in one hour is:
\[ 60 \frac{21}{28} \text{ km} \]

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