Two trains of the same length are running on parallel tracks in the same direction at 44 km h and 32 km/h. The faster train passes the other train in 72 seconds. What is the sum of the lengths (in m) of both trains?

Options

A. 240
B. 200
C. 190
D. 250

Answer

To solve the problem, we need to find the sum of the lengths of two trains moving in the same direction. Let's break it down step by step.

### Step 1: Determine the speeds of the trains
The speeds of the two trains are given as:
- Speed of the faster train = 44 km/h
- Speed of the slower train = 32 km/h

### Step 2: Calculate the relative speed
Since both trains are moving in the same direction, the relative speed is the difference between their speeds.

\[ \text{Relative Speed} = \text{Speed of Faster Train} - \text{Speed of Slower Train} \]
\[ \text{Relative Speed} = 44 \text{ km/h} - 32 \text{ km/h} = 12 \text{ km/h} \]

### Step 3: Convert the relative speed to meters per second
To work with the time given in seconds, we need to convert the speed from km/h to m/s. The conversion factor is:

\[ 1 \text{ km/h} = \frac{1000 \text{ m}}{3600 \text{ s}} = \frac{5}{18} \text{ m/s} \]

Now, converting 12 km/h to m/s:

\[ \text{Relative Speed in m/s} = 12 \times \frac{5}{18} = \frac{60}{18} = \frac{10}{3} \text{ m/s} \]

### Step 4: Use the formula for distance
The distance covered when one train passes the other is equal to the sum of their lengths. The formula relating speed, distance, and time is:

\[ \text{Distance} = \text{Speed} \times \text{Time} \]

In this case, the time taken to pass each other is given as 72 seconds. Thus, we can express the total distance (sum of lengths of both trains) as:

\[ \text{Sum of Lengths} = \text{Relative Speed} \times \text{Time} \]
\[ \text{Sum of Lengths} = \left(\frac{10}{3} \text{ m/s}\right) \times 72 \text{ s} \]

### Step 5: Calculate the sum of lengths
Now, we can calculate the sum of lengths:

\[ \text{Sum of Lengths} = \frac{10}{3} \times 72 = \frac{720}{3} = 240 \text{ m} \]

### Final Answer
The sum of the lengths of both trains is **240 meters**.

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