The distance between two stations P and Q is 110 km. A train with speed of 20 km/h leaves station P at 7:00 am towards station Q. Another train with speed of 25km/h leaves station Q at 8:00 am to wards station P.Then, at what time both trains meet?

Answer

To solve the problem step by step, we will determine the time at which both trains meet.

### Step 1: Calculate the distance covered by Train 1 before Train 2 starts.
Train 1 leaves Station P at 7:00 AM and travels at a speed of 20 km/h. Train 2 leaves Station Q at 8:00 AM. Therefore, Train 1 travels for 1 hour before Train 2 starts.

**Distance covered by Train 1 in 1 hour:**
\[ \text{Distance} = \text{Speed} \times \text{Time} = 20 \text{ km/h} \times 1 \text{ h} = 20 \text{ km} \]

### Step 2: Determine the remaining distance between the two trains when Train 2 starts.
The total distance between stations P and Q is 110 km. After Train 1 has traveled 20 km, the remaining distance is:

\[ \text{Remaining distance} = 110 \text{ km} - 20 \text{ km} = 90 \text{ km} \]

### Step 3: Calculate the combined speed of both trains.
Train 1 continues to travel towards Q at 20 km/h, and Train 2 travels towards P at 25 km/h. The combined speed of both trains is:

\[ \text{Combined speed} = \text{Speed of Train 1} + \text{Speed of Train 2} = 20 \text{ km/h} + 25 \text{ km/h} = 45 \text{ km/h} \]

### Step 4: Calculate the time taken for both trains to meet.
To find the time taken to cover the remaining distance of 90 km at a combined speed of 45 km/h, we use the formula:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{90 \text{ km}}{45 \text{ km/h}} = 2 \text{ hours} \]

### Step 5: Determine the meeting time.
Since Train 2 starts at 8:00 AM and it takes 2 hours for both trains to meet, the meeting time is:

\[ \text{Meeting time} = 8:00 \text{ AM} + 2 \text{ hours} = 10:00 \text{ AM} \]

### Final Answer:
Both trains will meet at **10:00 AM**.

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