A train leaves Delhi at 5 a.m. and reaches Kanpur at 10 a.m. Another train leaves Kanpur at 7 a.m. and reaches Delhi at 2 p.m. At what time do the two trains meet?

Options

A. 8.45am
B. 3.45p.m
C. 6.45a.m
D. data inadequate

Answer

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

### Step 1: Determine the distance between Delhi and Kanpur
Let's assume the distance between Delhi and Kanpur is \( D \) kilometers. For simplicity, we will use \( D = 35 \) km as suggested in the transcript.

### Step 2: Calculate the speed of the first train
The first train leaves Delhi at 5 a.m. and reaches Kanpur at 10 a.m. This means it takes 5 hours to cover the distance of 35 km.

\[ \text{Speed of first train} = \frac{\text{Distance}}{\text{Time}} = \frac{35 \text{ km}}{5 \text{ hours}} = 7 \text{ km/h} \]

### Step 3: Calculate the speed of the second train
The second train leaves Kanpur at 7 a.m. and reaches Delhi at 2 p.m. This means it takes 7 hours to cover the same distance of 35 km.

\[ \text{Speed of second train} = \frac{\text{Distance}}{\text{Time}} = \frac{35 \text{ km}}{7 \text{ hours}} = 5 \text{ km/h} \]

### Step 4: Set up the equation for the meeting point
Let \( t \) be the time in hours after 5 a.m. when the two trains meet.

- The distance covered by the first train after \( t \) hours is \( 7t \) km.
- The second train starts at 7 a.m., which is 2 hours after the first train has started. Therefore, it travels for \( t - 2 \) hours (only if \( t \) is greater than 2) and covers a distance of \( 5(t - 2) \) km.

At the meeting point, the total distance covered by both trains will equal the distance between Delhi and Kanpur:

\[ 7t + 5(t - 2) = 35 \]

### Step 5: Solve the equation
Expanding the equation:

\[ 7t + 5t - 10 = 35 \]
\[ 12t - 10 = 35 \]
\[ 12t = 45 \]
\[ t = \frac{45}{12} = 3.75 \text{ hours} \]

### Step 6: Determine the meeting time
Since \( t = 3.75 \) hours after 5 a.m., we can convert this into hours and minutes:

\[ 3.75 \text{ hours} = 3 \text{ hours} + 0.75 \text{ hours} = 3 \text{ hours} + 45 \text{ minutes} \]

Adding this to 5 a.m.:

\[ 5:00 \text{ a.m.} + 3 \text{ hours} + 45 \text{ minutes} = 8:45 \text{ a.m.} \]

### Conclusion
The two trains meet at **8:45 a.m.**

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