Two trains start simultaneously from two tunnels towards each other. The first train covers 8% of the distance between the two tunnels in 3 hours, the second train covered 7/120 of the distance in 2 hours 30 minutes. Find the speed (feet/h) of the second train. If the first train travelled 800 feet to the meeting point:

Answer

To solve the problem step by step, we will follow the information given in the question and the video transcript.

### Step 1: Define the total distance
Let the total distance between the two tunnels be represented as \( x \) feet.

### Step 2: Calculate the speed of the first train
The first train covers 8% of the distance in 3 hours. Therefore, the distance covered by the first train is:
\[ \text{Distance covered by Train A} = 0.08x \]
The speed of the first train (Train A) is given by:
\[ \text{Speed of Train A} = \frac{\text{Distance}}{\text{Time}} = \frac{0.08x}{3} \text{ feet/hour} \]

### Step 3: Calculate the distance covered by the second train
The second train covers \( \frac{7}{120} \) of the distance in 2 hours and 30 minutes (which is 2.5 hours). Therefore, the distance covered by the second train is:
\[ \text{Distance covered by Train B} = \frac{7}{120}x \]
The speed of the second train (Train B) is given by:
\[ \text{Speed of Train B} = \frac{\text{Distance}}{\text{Time}} = \frac{\frac{7}{120}x}{2.5} = \frac{7}{120}x \cdot \frac{1}{2.5} = \frac{7}{120}x \cdot \frac{10}{25} = \frac{7}{300}x \text{ feet/hour} \]

### Step 4: Distance covered by Train A to the meeting point
We know that Train A travels 800 feet to the meeting point. Therefore, we can set up the equation:
\[ 0.08x = 800 \]
From this, we can solve for \( x \):
\[ x = \frac{800}{0.08} = 10000 \text{ feet} \]

### Step 5: Calculate the distance covered by Train B to the meeting point
The distance covered by Train B to the meeting point is:
\[ \text{Distance covered by Train B} = x - 800 = 10000 - 800 = 9200 \text{ feet} \]

### Step 6: Set up the equation for equal time taken
Since both trains meet at the same point, the time taken by both trains to reach the meeting point is equal. Therefore, we can equate the time taken by both trains:
\[ \text{Time taken by Train A} = \frac{800}{\frac{0.08 \cdot 10000}{3}} = \frac{800 \cdot 3}{800} = 3 \text{ hours} \]
\[ \text{Time taken by Train B} = \frac{9200}{\frac{7}{300} \cdot 10000} \]

### Step 7: Solve for the speed of Train B
Now we can calculate the speed of Train B:
\[ \text{Speed of Train B} = \frac{7}{300} \cdot 10000 = \frac{70000}{300} = \frac{700}{3} \approx 233.33 \text{ feet/hour} \]

### Final Answer
The speed of the second train is approximately \( 233.33 \) feet/hour.