Distance between two stations is 450km. A train from A starts moving towards B at the speed of 15km/ h another train from B starts moving towards A 20 minutes before the first train with the speed of 20km/ h. Find at what distance from A will they meet each other.

Answer

To solve the problem step-by-step, let's break it down into manageable parts.

### Step 1: Convert the time into hours
The train from B starts 20 minutes before the train from A. We need to convert this time into hours since the speed is given in km/h.

\[ 20 \text{ minutes} = \frac{20}{60} \text{ hours} = \frac{1}{3} \text{ hours} \]

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

### Step 2: Calculate the distance traveled by the train from B in 20 minutes
Now, we can calculate how far the train from B travels in that time.

\[ \text{Distance} = \text{Speed} \times \text{Time} = 20 \text{ km/h} \times \frac{1}{3} \text{ hours} = \frac{20}{3} \text{ km} \approx 6.67 \text{ km} \]

**Hint:** Use the formula for distance, which is speed multiplied by time.

### Step 3: Calculate the remaining distance between the two trains when the train from A starts
The total distance between the two stations is 450 km. After the train from B travels for 20 minutes, the remaining distance to be covered is:

\[ \text{Remaining Distance} = 450 \text{ km} - \frac{20}{3} \text{ km} = \frac{1350 - 20}{3} = \frac{1330}{3} \text{ km} \approx 443.33 \text{ km} \]

**Hint:** Subtract the distance traveled by the first train from the total distance to find the remaining distance.

### Step 4: Calculate the relative speed of the two trains
When both trains are moving towards each other, their speeds add up. The speed of the train from A is 15 km/h and from B is 20 km/h.

\[ \text{Relative Speed} = 15 \text{ km/h} + 20 \text{ km/h} = 35 \text{ km/h} \]

**Hint:** When two objects move towards each other, their speeds combine.

### Step 5: Calculate the time taken for the two trains to meet
Now, we can find out how long it will take for the two trains to meet after the train from A starts.

\[ \text{Time} = \frac{\text{Remaining Distance}}{\text{Relative Speed}} = \frac{\frac{1330}{3} \text{ km}}{35 \text{ km/h}} = \frac{1330}{3 \times 35} = \frac{1330}{105} \text{ hours} \approx 12.67 \text{ hours} \]

**Hint:** Use the formula for time, which is distance divided by speed.

### Step 6: Calculate the distance traveled by the train from A before they meet
Now, we can find out how far the train from A travels in that time.

\[ \text{Distance from A} = \text{Speed of A} \times \text{Time} = 15 \text{ km/h} \times \frac{1330}{105} \text{ hours} = \frac{19950}{105} \text{ km} \approx 189.57 \text{ km} \]

**Hint:** Again, use the distance formula (speed × time) to find how far the train travels.

### Final Answer
The distance from station A at which the two trains meet is approximately **189.57 km**.

---