A train leaves station x and travels east at 30 kph. Two hours later,another train leaves the same station and travels in the same direction on a parallel track at 45kph. At what point will the faster train overtake the slower train?

in 2 hours, the 1st train has covered 60 km.

the 2nd train goes 15km/hr faster, so it will take 60/15 = 4 hours to make up the distance.

To find the point at which the faster train overtakes the slower train, we need to determine the time it takes for the faster train to catch up to the slower train.

Let's assume the distance between the two trains when the faster train starts is D.

Since the slower train has a head start of 2 hours, it will have already traveled a distance of 30 kph * 2 hours = 60 km when the faster train starts.

So, the distance between the two trains when the faster train starts is D - 60 km.

Now, let's determine the time it takes for the faster train to catch up to the slower train. We can use the formula:

Time = Distance / Speed

The distance the faster train needs to cover to catch up to the slower train is D km.

The speed of the faster train relative to the slower train is 45 kph - 30 kph = 15 kph.

Therefore, the time it takes for the faster train to catch up to the slower train is:

Time = D km / 15 kph

Since the faster train starts 2 hours later, the total time it takes for the faster train to catch up to the slower train is:

Total Time = 2 hours + Time

Now, since we know that Time = D km / 15 kph, we can substitute this into the equation:

Total Time = 2 hours + D km / 15 kph

To find the point at which the faster train overtakes the slower train, we need to determine the total distance covered by the faster train. This can be calculated using the formula:

Distance = Speed * Time

The distance covered by the faster train is:

Distance = 45 kph * Total Time = 45 kph * (2 hours + D km / 15 kph)

Since the slower train already traveled a distance of 60 km when the faster train starts, the point at which the faster train overtakes the slower train can be found by adding the distance covered by the faster train to this distance:

Point of Overtake = 60 km + 45 kph * (2 hours + D km / 15 kph)

Simplifying this equation, we get:

Point of Overtake = 60 km + 90 km + 3D km

Therefore, the faster train will overtake the slower train at a point that is 150 km + 3D km from station X, depending on the value of D.

To find the point at which the faster train overtakes the slower train, we need to determine the distance the slower train has traveled in the time it takes for the faster train to catch up.

Let's break it down step by step:

1. Determine the time it takes for the faster train to catch up: The faster train is traveling at a speed of 45 kph, while the slower train is traveling at a speed of 30 kph. The faster train needs to cover the initial distance between the two trains, which is the distance traveled by the slower train in the initial 2 hours. We can calculate this distance by multiplying the slower train's speed (30 kph) by the time (2 hours) it has been traveling. Thus, the initial distance would be 30 kph * 2 hours = 60 kilometers.

2. Calculate the relative speed of the two trains: The relative speed of the two trains is the difference between their speeds. In this case, the relative speed would be 45 kph - 30 kph = 15 kph.

3. Determine the time it takes for the faster train to catch up: Now, we can determine the time it takes for the faster train to close the initial distance of 60 kilometers between the two trains. To do this, we divide the initial distance by the relative speed. Thus, the time it takes for the faster train to catch up would be 60 kilometers / 15 kph = 4 hours.

4. Calculate the distance traveled by the faster train: Now that we know it takes 4 hours for the faster train to catch up to the slower train, we can calculate the distance it has traveled during this time. Since the faster train is traveling at a speed of 45 kph, the distance traveled would be 45 kph * 4 hours = 180 kilometers.

Therefore, the faster train will overtake the slower train at a point 180 kilometers from the station.