Two trains for Mumbai leave Delhi at 6 a.m. and 6 : 45 am and travel at 100 kmph and 136 kmph respectively. How many kilometres from Delhi will the two trains be together

Options

A. 262.4 km
B. 260 km
C. 283.33 km
D. 275 km

Answer

To solve the problem of when the two trains will meet, we can follow these steps:

### Step 1: Calculate the time difference in departure
The first train leaves at 6:00 a.m. and the second train leaves at 6:45 a.m. The time difference is:
\[ 6:45 \text{ a.m.} - 6:00 \text{ a.m.} = 45 \text{ minutes} \]
Convert this into hours:
\[ 45 \text{ minutes} = \frac{45}{60} = \frac{3}{4} \text{ hours} \]

**Hint:** Remember that to convert minutes to hours, divide by 60.

### Step 2: Assume the distance where they meet
Let the distance from Delhi where the two trains meet be \( x \) kilometers.

### Step 3: Set up the time equations for both trains
- For the second train (traveling at 136 km/h), let the time taken to reach the meeting point be \( t \) hours.
- For the first train (traveling at 100 km/h), the time taken will be \( t + \frac{3}{4} \) hours (since it leaves 45 minutes earlier).

### Step 4: Write the distance equations
Using the formula \( \text{Distance} = \text{Speed} \times \text{Time} \):
- For the second train:
\[ x = 136t \]
- For the first train:
\[ x = 100\left(t + \frac{3}{4}\right) \]

### Step 5: Set the equations equal to each other
Since both expressions equal \( x \), we can set them equal:
\[ 136t = 100\left(t + \frac{3}{4}\right) \]

### Step 6: Expand and simplify the equation
Expanding the right side:
\[ 136t = 100t + 100 \times \frac{3}{4} \]
\[ 136t = 100t + 75 \]

### Step 7: Solve for \( t \)
Rearranging the equation:
\[ 136t - 100t = 75 \]
\[ 36t = 75 \]
\[ t = \frac{75}{36} = 2.083 \text{ hours} \]

### Step 8: Calculate the distance \( x \)
Now substituting \( t \) back into the equation for distance:
\[ x = 136t = 136 \times 2.083 \]
Calculating this gives:
\[ x \approx 283.33 \text{ kilometers} \]

### Final Answer
The two trains will be together approximately **283.33 kilometers** from Delhi.

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