Two trains Punjab mail and Lucknow mail starts simultaneously from Patiyala and Lakhimpur respectively towards each other with the speed of 40 km/h and 60 km/h respectively on the same track Lakhimpur is 500 km due east of Patiyala. A plane starts flying at 200 km/h at the same time from Patiyala to Jalandhar. Jalandhar is 100 km due north of Patiyala. After travelling sometime two trains Punjab mail and Lucknow mail collides with each other. The plane moves continuously to and fro between Patiyala to Jalandhar till the collision of the trains. How far would the plane have travelled?

Options

A. 100 km
B. 1000 km
C. 2000 km
D. can't be determined

Answer

To solve the problem, we need to find out how far the plane travels before the two trains collide. Here’s a step-by-step solution:

### Step 1: Determine the relative speed of the trains
The speed of Punjab Mail (from Patiala) is 40 km/h, and the speed of Lucknow Mail (from Lakhimpur) is 60 km/h. Since they are moving towards each other, we can add their speeds to find the relative speed.

**Relative Speed = Speed of Punjab Mail + Speed of Lucknow Mail**
\[ \text{Relative Speed} = 40 \text{ km/h} + 60 \text{ km/h} = 100 \text{ km/h} \]

### Step 2: Calculate the time until the trains collide
The distance between Patiala and Lakhimpur is 500 km. We can use the formula for time, which is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Substituting the values:
\[ \text{Time} = \frac{500 \text{ km}}{100 \text{ km/h}} = 5 \text{ hours} \]

### Step 3: Calculate the distance traveled by the plane
The plane flies from Patiala to Jalandhar at a speed of 200 km/h. We can find out how far the plane travels in the time until the trains collide.

Using the formula for distance:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Substituting the values:
\[ \text{Distance} = 200 \text{ km/h} \times 5 \text{ hours} = 1000 \text{ km} \]

### Final Answer
The plane would have traveled **1000 km** before the collision of the trains.

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