Two trains start from station A and B and travel towards each other at speeds of 16 miles /hour and 21 miles / hour respectively. At the time of their meeting, the second train has travelled 60 miles more than the first. Find the distance between A and B (in miles).

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript:

### Step 1: Understand the Problem
Two trains are traveling towards each other from two stations, A and B. Train 1 travels at a speed of 16 miles/hour, and Train 2 travels at a speed of 21 miles/hour. When they meet, Train 2 has traveled 60 miles more than Train 1.

### Step 2: Set Up the Variables
Let:
- Distance traveled by Train 1 = \( d_1 \)
- Distance traveled by Train 2 = \( d_2 \)

From the problem, we know:
\[ d_2 = d_1 + 60 \]

### Step 3: Relate Distance to Speed and Time
Since both trains meet at the same time, we can express the time taken by both trains to meet:
- Time taken by Train 1 = \( \frac{d_1}{16} \)
- Time taken by Train 2 = \( \frac{d_2}{21} \)

Since the times are equal:
\[ \frac{d_1}{16} = \frac{d_2}{21} \]

### Step 4: Substitute \( d_2 \) in the Time Equation
Substituting \( d_2 \) from Step 2 into the time equation:
\[ \frac{d_1}{16} = \frac{d_1 + 60}{21} \]

### Step 5: Cross-Multiply to Solve for \( d_1 \)
Cross-multiplying gives:
\[ 21d_1 = 16(d_1 + 60) \]

Expanding the right side:
\[ 21d_1 = 16d_1 + 960 \]

### Step 6: Rearranging the Equation
Rearranging the equation to isolate \( d_1 \):
\[ 21d_1 - 16d_1 = 960 \]
\[ 5d_1 = 960 \]

### Step 7: Solve for \( d_1 \)
Dividing both sides by 5:
\[ d_1 = \frac{960}{5} = 192 \text{ miles} \]

### Step 8: Find \( d_2 \)
Now, using \( d_2 = d_1 + 60 \):
\[ d_2 = 192 + 60 = 252 \text{ miles} \]

### Step 9: Calculate Total Distance Between A and B
The total distance between A and B is:
\[ \text{Total Distance} = d_1 + d_2 = 192 + 252 = 444 \text{ miles} \]

### Final Answer
The distance between stations A and B is **444 miles**.

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