A train leaves from a station and moves at 40 km/hr. After 2 hours, another train leaves from the same station and moves in the same direction at a certain speed. If the second train catches up with the first train in 4 hours, what is the speed of the second train? Options are (a) 55 km/hr (b) 50 km/hr (c) 60 km/hr (d) 65 km/hr .

Options

A. 55 km/hr
B. 50 km/hr
C. 60 km/hr
D. 65 km/hr

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Determine the distance traveled by the first train.
The first train leaves the station and travels at a speed of 40 km/hr for 2 hours before the second train departs.

**Distance = Speed × Time**
- Speed of the first train = 40 km/hr
- Time traveled by the first train before the second train leaves = 2 hours

**Distance traveled by the first train = 40 km/hr × 2 hours = 80 km**

### Step 2: Understand the scenario when the second train starts.
After 2 hours, the second train leaves the station and travels in the same direction as the first train. The second train catches up with the first train in 4 hours.

### Step 3: Calculate the distance covered by the first train during the 4 hours after the second train departs.
During the 4 hours that the second train is traveling, the first train continues to move.

**Distance = Speed × Time**
- Time traveled by the first train after the second train departs = 4 hours
- Speed of the first train = 40 km/hr

**Distance traveled by the first train in these 4 hours = 40 km/hr × 4 hours = 160 km**

### Step 4: Calculate the total distance traveled by the first train when the second train catches up.
The total distance traveled by the first train when the second train catches up is the distance it traveled before the second train left plus the distance it traveled after.

**Total distance = Distance before + Distance after**
- Distance before = 80 km
- Distance after = 160 km

**Total distance = 80 km + 160 km = 240 km**

### Step 5: Calculate the speed of the second train.
The second train travels for 4 hours to catch up with the first train, covering the same total distance of 240 km.

**Speed = Distance / Time**
- Distance traveled by the second train = 240 km
- Time taken by the second train = 4 hours

**Speed of the second train = 240 km / 4 hours = 60 km/hr**

### Conclusion:
The speed of the second train is **60 km/hr**.

### Options:
(a) 55 km/hr
(b) 50 km/hr
(c) 60 km/hr
(d) 65 km/hr

The correct answer is **(c) 60 km/hr**.

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