A train leaves a station and travels north at a speed of 45mph. Four hours later, a second train leaves on a parallel track and travels north at 105 mph. How far from the station will they meet?

The trains will meet ________ miles away from the station

Using distance = rate x time

105t = 45(t+4)
105t = 45t + 180
60t = 180
t = 3

distance covered by each
= 105(3) = 45(7) = 315 miles

Well, let's see. If the second train is going 105 mph and the first train has already been chugging along for four hours at 45 mph, it means that the first train has a head start. In those four hours, the first train would have covered a distance of 45 mph × 4 hours = 180 miles.

Now, let's do some math magic. We know that the second train is catching up to the first train at a speed of 105 mph - 45 mph = 60 mph. So, we need to figure out how long it will take for the second train to catch up.

To do that, we'll take the distance the first train has already covered (180 miles) and divide it by the relative speed of the two trains (60 mph). 180 miles ÷ 60 mph = 3 hours.

So, it will take the second train 3 hours to catch up to the first train after it departs. In those 3 hours, the second train would have traveled 105 mph × 3 hours = 315 miles.

Now, to figure out how far from the station they meet, we can add the distance the second train traveled to the distance the first train traveled before they met: 180 miles + 315 miles = 495 miles.

Therefore, the trains will meet 495 miles away from the station. I hope they bring a good playlist for that journey!

To solve this question, we can use the concept of relative motion. Since both trains are traveling in the same direction, we can consider the second train as the reference point and calculate the distance covered by both trains relative to the second train.

The first train has a head start of 45 mph × 4 hours = 180 miles.

Let's determine the time it takes for the two trains to meet.

Let 't' be the time it takes for the second train to catch up to the first train.

Since the second train travels at 105 mph and the first train travels at 45 mph, the relative speed of the second train catching up to the first train is 105 mph - 45 mph = 60 mph.

Using the formula distance = speed × time, we can write the equation:
60t = 180

Dividing both sides of the equation by 60, we get:
t = 3

So, it will take the second train 3 hours to catch up to the first train.

Now, let's calculate the distance traveled by the second train in those 3 hours:
Distance = speed × time = 105 mph × 3 hours = 315 miles.

Therefore, the two trains will meet 315 miles away from the station.

To find the distance from the station where the two trains will meet, we need to determine the time it takes for the second train to catch up to the first train.

Let's first calculate the distance the first train travels during the four hours it leaves before the second train starts. The formula to calculate distance is:

Distance = Speed * Time

For the first train:
Distance1 = Speed1 * Time1
Distance1 = 45 mph * 4 hours
Distance1 = 180 miles

Since the first train has already traveled 180 miles when the second train starts, the second train needs to cover this distance to catch up.

Now, let's determine the time it takes for the second train to catch up to the first train. Since both trains are traveling at the same speed but the second train has a head start of 180 miles, we can set up a simple equation:

Distance2 = Speed2 * Time2
180 miles = 105 mph * Time2

Solving for Time2 gives us:
Time2 = 180 miles / 105 mph
Time2 ≈ 1.714 hours

Therefore, it will take approximately 1.714 hours for the second train to catch up to the first train.

To find the total distance from the station where the trains meet, we can calculate the distance traveled by the second train during this time:

Distance2 = Speed2 * Time2
Distance2 = 105 mph * 1.714 hours
Distance2 ≈ 180 miles

Since the second train covered the same distance as the first train's head start, they will meet approximately 180 miles away from the station.