Rubi goes to a multiplex at the speed of 3km/hr to see a movie and reaches 5 minutes late. If she travels at the speed of 4km/hr she reaches 5 minutes early. Then the distance of the multiplex from her starting point is

Options

A. 2km
B. 5km
C. 2metre
D. 5 metre

Answer

To solve the problem, we need to find the distance of the multiplex from Rubi's starting point based on the information given about her travel times at different speeds.

### Step-by-Step Solution:

1. **Define Variables**:
Let the distance to the multiplex be \( d \) kilometers.

2. **Calculate Time Taken at Different Speeds**:
- When Rubi travels at 3 km/hr and is 5 minutes late, the time taken can be expressed as:
\[ \text{Time at 3 km/hr} = \frac{d}{3} \text{ hours} \]
- When Rubi travels at 4 km/hr and is 5 minutes early, the time taken can be expressed as:
\[ \text{Time at 4 km/hr} = \frac{d}{4} \text{ hours} \]

3. **Convert Minutes to Hours**:
Since 5 minutes is \(\frac{5}{60} = \frac{1}{12}\) hours, we can set up the equations based on the information given:
- The time taken at 3 km/hr is 5 minutes (or \(\frac{1}{12}\) hours) more than the time it should take:
\[ \frac{d}{3} = T + \frac{1}{12} \]
- The time taken at 4 km/hr is 5 minutes (or \(\frac{1}{12}\) hours) less than the time it should take:
\[ \frac{d}{4} = T - \frac{1}{12} \]

4. **Set Up the Equations**:
From the above two equations, we can eliminate \( T \):
- Rearranging both equations gives us:
\[ T = \frac{d}{3} - \frac{1}{12} \quad \text{(1)} \]
\[ T = \frac{d}{4} + \frac{1}{12} \quad \text{(2)} \]

5. **Equate the Two Expressions for T**:
Set the two expressions for \( T \) equal to each other:
\[ \frac{d}{3} - \frac{1}{12} = \frac{d}{4} + \frac{1}{12} \]

6. **Clear the Fractions**:
Multiply through by 12 to eliminate the denominators:
\[ 12 \left(\frac{d}{3}\right) - 1 = 12 \left(\frac{d}{4}\right) + 1 \]
This simplifies to:
\[ 4d - 1 = 3d + 1 \]

7. **Solve for d**:
Rearranging gives:
\[ 4d - 3d = 1 + 1 \]
\[ d = 2 \]

8. **Conclusion**:
The distance of the multiplex from Rubi's starting point is \( \boxed{2} \) kilometers.