Two buses are moving towards each other with speed of 20 km/hr and 34km/hr respectively. What will be the distance (in metres) between the two buses one second before they collide?

Options

A. 21
B. 18
C. 12
D. 15

Answer

To solve the problem of finding the distance between two buses one second before they collide, we can follow these steps:

### Step 1: Determine the speeds of the buses
The speeds of the two buses are given as:
- Bus 1: 20 km/hr
- Bus 2: 34 km/hr

### Step 2: Calculate the relative speed
Since the buses are moving towards each other, we can find the relative speed by adding their speeds together:
\[ \text{Relative Speed} = \text{Speed of Bus 1} + \text{Speed of Bus 2} = 20 \text{ km/hr} + 34 \text{ km/hr} = 54 \text{ km/hr} \]

### Step 3: Convert the relative speed from km/hr to m/s
To convert km/hr to m/s, we use the conversion factor \( \frac{5}{18} \):
\[ \text{Relative Speed in m/s} = 54 \text{ km/hr} \times \frac{5}{18} = 15 \text{ m/s} \]

### Step 4: Calculate the distance covered in 1 second
To find the distance between the two buses one second before they collide, we can use the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Here, the speed is the relative speed (15 m/s) and the time is 1 second:
\[ \text{Distance} = 15 \text{ m/s} \times 1 \text{ s} = 15 \text{ meters} \]

### Final Answer
The distance between the two buses one second before they collide is **15 meters**.

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