A and B travel the same distance at speed of 9km/hr and 10km/hr respectively. If A takes 36 minutes more than B, the distance travelled by each is

Options

A. 48km
B. 54km
C. 60km
D. 66km

Answer

To solve the problem, we need to find the distance traveled by A and B given their speeds and the time difference in their travel.

### Step-by-Step Solution:

1. **Define Variables**:
Let the distance traveled by both A and B be \( x \) kilometers.

2. **Calculate Time Taken**:
- The time taken by A to travel the distance \( x \) at a speed of 9 km/hr is:
\[ \text{Time}_A = \frac{x}{9} \text{ hours} \]
- The time taken by B to travel the same distance \( x \) at a speed of 10 km/hr is:
\[ \text{Time}_B = \frac{x}{10} \text{ hours} \]

3. **Set Up the Equation**:
According to the problem, A takes 36 minutes more than B. We need to convert 36 minutes into hours:
\[ 36 \text{ minutes} = \frac{36}{60} \text{ hours} = 0.6 \text{ hours} \]
Therefore, we can set up the equation:
\[ \text{Time}_A = \text{Time}_B + 0.6 \]
Substituting the expressions for time:
\[ \frac{x}{9} = \frac{x}{10} + 0.6 \]

4. **Solve the Equation**:
To eliminate the fractions, we can multiply the entire equation by 90 (the least common multiple of 9 and 10):
\[ 90 \cdot \frac{x}{9} = 90 \cdot \frac{x}{10} + 90 \cdot 0.6 \]
Simplifying this gives:
\[ 10x = 9x + 54 \]
Rearranging the equation:
\[ 10x - 9x = 54 \]
\[ x = 54 \]

5. **Conclusion**:
The distance traveled by each A and B is \( 54 \) kilometers.