Two trains leave Meerut at the difference of 4 hours. The first train leaves at 8 am at 40 km/h and the faster train leaves later at 60 km/h in the same direction.
When the faster train will overtake the slower train?

Options

A. `4` pm
B. `2` pm
C. `8` pm
D. `6:30` pm

Answer

To solve the problem of when the faster train will overtake the slower train, we can follow these steps:

### Step 1: Determine the time difference and the speed of each train.
- The first train leaves Meerut at 8 AM and travels at a speed of 40 km/h.
- The second train leaves 4 hours later, at 12 PM, and travels at a speed of 60 km/h.

**Hint:** Identify the time difference and the speeds of both trains to set up the problem.

### Step 2: Calculate the distance covered by the first train before the second train starts.
- The first train travels for 4 hours before the second train starts.
- Distance = Speed × Time = 40 km/h × 4 hours = 160 km.

**Hint:** Use the formula for distance to find out how far the first train has traveled when the second train starts.

### Step 3: Set up the equation for when the faster train overtakes the slower train.
- Let \( t \) be the time in hours after the second train starts.
- In that time, the first train will have traveled an additional distance of \( 40t \) km.
- The second train will have traveled \( 60t \) km.
- The distance covered by the first train when the second train starts is 160 km, so we can set up the equation:
\[ 160 + 40t = 60t \]

**Hint:** Write an equation that relates the distances traveled by both trains after the second train starts.

### Step 4: Solve the equation for \( t \).
- Rearranging the equation gives:
\[ 160 = 60t - 40t \]
\[ 160 = 20t \]
\[ t = \frac{160}{20} = 8 \text{ hours} \]

**Hint:** Isolate \( t \) to find out how long it takes for the second train to catch up.

### Step 5: Determine the time of day when the faster train overtakes the slower train.
- The second train starts at 12 PM, and it takes 8 hours to catch up.
- Therefore, the time when the second train overtakes the first train is:
\[ 12 \text{ PM} + 8 \text{ hours} = 8 \text{ PM} \]

**Hint:** Add the time taken to the start time of the second train to find the final answer.

### Final Answer:
The faster train will overtake the slower train at **8 PM**.