Two trains start from station A and B and travel towards each other at speed 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. The distance between A and B (in miles) is

Options

A. 444
B. 496
C. 333
D. 540

Answer

To solve the problem step by step, we will use the information provided about the speeds of the trains and the distance traveled by each train at the time of their meeting.

### Step 1: Define the Variables
Let:
- Speed of Train A = 16 miles/hour
- Speed of Train B = 21 miles/hour
- Distance traveled by Train A = \(d_A\)
- Distance traveled by Train B = \(d_B\)

### Step 2: Set Up the Relationship Between Distances
According to the problem, at the time of their meeting, Train B has traveled 60 miles more than Train A. Therefore, we can express this relationship as:
\[ d_B = d_A + 60 \]

### Step 3: Relate Distances to Time
Since both trains are traveling towards each other, they will meet after the same amount of time. We can express the time taken by both trains to meet as:
\[ \text{Time} = \frac{d_A}{\text{Speed of A}} = \frac{d_B}{\text{Speed of B}} \]

Substituting the speeds:
\[ \frac{d_A}{16} = \frac{d_B}{21} \]

### Step 4: Substitute \(d_B\) in Terms of \(d_A\)
From Step 2, we know that \(d_B = d_A + 60\). We can substitute this into the time equation:
\[ \frac{d_A}{16} = \frac{d_A + 60}{21} \]

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

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

### Step 6: Isolate \(d_A\)
Now, we will isolate \(d_A\):
\[ 21d_A - 16d_A = 960 \]
\[ 5d_A = 960 \]
\[ d_A = \frac{960}{5} = 192 \text{ miles} \]

### Step 7: Find \(d_B\)
Now that we have \(d_A\), we can find \(d_B\):
\[ d_B = d_A + 60 = 192 + 60 = 252 \text{ miles} \]

### Step 8: Calculate the Total Distance Between A and B
The total distance between stations A and B is the sum of the distances traveled by both trains:
\[ \text{Total Distance} = d_A + d_B = 192 + 252 = 444 \text{ miles} \]

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

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