Jammutavi express leaves jammu for kanya kumari at 120 km/h and returns to jammu at 80 km/h what is the average speed of the train during the whole journey?if the total time taken by the train is 25 hours what is the distance between these two places?

Options

A. 1365.5 km
B. 1369 km
C. 1200 km
D. can't be determined

Answer

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

### Step 1: Understand the speeds and the journey
The Jammu Tavi Express travels from Jammu to Kanyakumari at a speed of 120 km/h and returns at a speed of 80 km/h.

### Step 2: Use the formula for average speed
The average speed for a round trip can be calculated using the formula:
\[ \text{Average Speed} = \frac{2 \times S_1 \times S_2}{S_1 + S_2} \]
where \( S_1 \) is the speed to Kanyakumari and \( S_2 \) is the speed back to Jammu.

### Step 3: Substitute the values into the formula
Substituting the values into the formula:
\[ \text{Average Speed} = \frac{2 \times 120 \times 80}{120 + 80} \]
Calculating the denominator:
\[ 120 + 80 = 200 \]
Now substituting back:
\[ \text{Average Speed} = \frac{2 \times 120 \times 80}{200} \]

### Step 4: Calculate the numerator
Calculating the numerator:
\[ 2 \times 120 \times 80 = 19200 \]
Now substituting this value:
\[ \text{Average Speed} = \frac{19200}{200} = 96 \text{ km/h} \]

### Step 5: Calculate the total distance using total time
We know the total time taken for the journey is 25 hours. The average speed we calculated is 96 km/h.

Using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Substituting the values:
\[ \text{Distance} = 96 \times 25 \]

### Step 6: Calculate the distance
Calculating the distance:
\[ \text{Distance} = 2400 \text{ km} \]

### Final Answer
The distance between Jammu and Kanyakumari is **2400 km**.

---