A man walking at the rate of 5km/hr. crosses a bridge in 15 minutes. The length of the brige (in metres) is :

Options

A. `600`
B. `750`
C. `1000`
D. `1250`

Answer

To find the length of the bridge that a man crosses while walking, we can follow these steps:

### Step-by-Step Solution:

1. **Convert the Speed from km/hr to m/min**:
- The speed of the man is given as 5 km/hr.
- To convert this speed into meters per minute, we use the conversion factor:
\[ 1 \text{ km} = 1000 \text{ meters} \]
\[ 1 \text{ hour} = 60 \text{ minutes} \]
- Therefore, the speed in meters per minute is:
\[ \text{Speed} = 5 \text{ km/hr} = \frac{5 \times 1000 \text{ meters}}{60 \text{ minutes}} = \frac{5000}{60} \text{ m/min} = \frac{250}{3} \text{ m/min} \]

2. **Determine the Time Taken to Cross the Bridge**:
- The time taken to cross the bridge is given as 15 minutes.

3. **Calculate the Length of the Bridge**:
- The length of the bridge can be calculated using the formula for distance:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
- Substituting the values we have:
\[ \text{Length of the bridge} = \left(\frac{250}{3} \text{ m/min}\right) \times 15 \text{ min} \]
- Simplifying this:
\[ = \frac{250 \times 15}{3} = \frac{3750}{3} = 1250 \text{ meters} \]

4. **Final Answer**:
- The length of the bridge is **1250 meters**.