The distance between two stations is 500km. A train starts from station A at 9 a.m and moves towards station B at 60 kmph. The other train leaves station B towards A at 10 a.m at the speed of 40 kmph. At what time will they cross each other?

Options

A. `3:36`pm
B. `12:45`pm
C. `2.24`pm
D. `1:36`pm

Answer

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

### Step 1: Determine the distance covered by the first train before the second train starts.
- The first train leaves station A at 9 a.m. and travels at a speed of 60 km/h.
- The second train leaves station B at 10 a.m.
- Therefore, the first train travels for 1 hour before the second train starts.

**Distance covered by the first train in 1 hour:**
\[ \text{Distance} = \text{Speed} \times \text{Time} = 60 \, \text{km/h} \times 1 \, \text{h} = 60 \, \text{km} \]

### Step 2: Calculate the remaining distance between the two trains when the second train starts.
- The total distance between the two stations is 500 km.
- After the first train has traveled 60 km, the remaining distance is:
\[ \text{Remaining Distance} = 500 \, \text{km} - 60 \, \text{km} = 440 \, \text{km} \]

### Step 3: Calculate the combined speed of both trains.
- The speed of the first train is 60 km/h and the speed of the second train is 40 km/h.
- When two objects move towards each other, their speeds add up.
\[ \text{Combined Speed} = 60 \, \text{km/h} + 40 \, \text{km/h} = 100 \, \text{km/h} \]

### Step 4: Calculate the time taken to cover the remaining distance.
- We need to find the time taken to cover the remaining 440 km at a combined speed of 100 km/h.
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{440 \, \text{km}}{100 \, \text{km/h}} = 4.4 \, \text{hours} \]

### Step 5: Convert the time from hours to hours and minutes.
- 4.4 hours can be converted to hours and minutes:
- The whole number part is 4 hours.
- The decimal part (0.4 hours) can be converted to minutes:
\[ 0.4 \times 60 \, \text{minutes} = 24 \, \text{minutes} \]
- Therefore, 4.4 hours is equivalent to 4 hours and 24 minutes.

### Step 6: Determine the time at which the trains will cross each other.
- The second train starts at 10 a.m. and it takes 4 hours and 24 minutes for the two trains to meet.
- Adding 4 hours and 24 minutes to 10 a.m.:
- 10:00 a.m. + 4 hours = 2:00 p.m.
- 2:00 p.m. + 24 minutes = 2:24 p.m.

### Final Answer:
The two trains will cross each other at **2:24 p.m.**.

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