Two bombs blast at an interval of 10 minutes. A person running away from that place hears the two blasts at an interval of 12 minutes. If speed of sound is 330 m/s find the speed of the person and the distance he covered by running away from the blast.

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the Time Difference
The two bombs explode at an interval of 10 minutes. However, the person running away hears the blasts at an interval of 12 minutes.

**Hint:** Calculate the difference in time between the two intervals.

### Step 2: Calculate the Time Difference
The time difference is:
\[ 12 \text{ minutes} - 10 \text{ minutes} = 2 \text{ minutes} \]

**Hint:** Convert the time difference from minutes to seconds.

### Step 3: Convert Minutes to Seconds
To convert 2 minutes into seconds:
\[ 2 \text{ minutes} \times 60 \text{ seconds/minute} = 120 \text{ seconds} \]

**Hint:** Use the formula for distance traveled to find the distance the sound traveled in this time.

### Step 4: Calculate the Distance the Sound Traveled
The speed of sound is given as 330 m/s. The distance traveled by sound in 120 seconds is calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
\[ \text{Distance} = 330 \text{ m/s} \times 120 \text{ seconds} = 39600 \text{ meters} \]

**Hint:** Now, we need to find the speed of the person running away from the blasts.

### Step 5: Calculate the Speed of the Person
The person hears the two blasts at an interval of 12 minutes, which is 720 seconds. The distance covered by the person is the same as the distance traveled by sound (39600 meters).

Using the formula for speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
\[ \text{Speed} = \frac{39600 \text{ meters}}{720 \text{ seconds}} \]

**Hint:** Simplify the fraction to find the speed.

### Step 6: Simplify the Speed Calculation
Calculating the speed:
\[ \text{Speed} = \frac{39600}{720} = 55 \text{ m/s} \]

### Final Answer
The speed of the person running away from the blast is **55 m/s**.

### Step 7: Calculate the Distance Covered by the Person
To find the distance covered by the person during the 12 minutes (720 seconds):
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
\[ \text{Distance} = 55 \text{ m/s} \times 720 \text{ seconds} = 39600 \text{ meters} \]

### Conclusion
The speed of the person is **55 m/s**, and the distance covered by the person is **39600 meters**.