Wind is blowing west to east along twoparallelracs. Two trais moving with the same speed in opposite directions on these tracks have the steam tracks. If one stream track isdouble than the other, what is the speed of each train ?

Options

A. Half that of wind
B. Equal to that of wind
C. Double that of wind
D. Three times that of wind

Answer

To solve the problem, let's break it down step by step.

### Step 1: Understand the Problem
We have two trains moving in opposite directions on two parallel tracks. One track is double the length of the other. The wind is blowing from west to east. We need to find the speed of each train.

### Step 2: Define Variables
- Let the speed of the trains be \( V \).
- Let the speed of the wind be \( W \).
- The length of the first track is \( X \).
- The length of the second track is \( 2X \).

### Step 3: Set Up Equations
For Train A (on the longer track of length \( 2X \)):
- The effective speed of Train A (moving with the wind) is \( V + W \).
- The time taken by Train A to cover \( 2X \) is given by:
\[ T = \frac{2X}{V + W} \]

For Train B (on the shorter track of length \( X \)):
- The effective speed of Train B (moving against the wind) is \( V - W \).
- The time taken by Train B to cover \( X \) is given by:
\[ T = \frac{X}{V - W} \]

### Step 4: Equate the Times
Since both trains take the same time to travel their respective distances, we can set the two equations for time equal to each other:
\[ \frac{2X}{V + W} = \frac{X}{V - W} \]

### Step 5: Simplify the Equation
Cross-multiplying gives:
\[ 2X(V - W) = X(V + W) \]
Dividing both sides by \( X \) (assuming \( X \neq 0 \)):
\[ 2(V - W) = V + W \]

### Step 6: Solve for \( V \)
Expanding and rearranging:
\[ 2V - 2W = V + W \]
\[ 2V - V = W + 2W \]
\[ V = 3W \]

### Conclusion
The speed of each train is \( V = 3W \), which means the speed of each train is three times the speed of the wind.