at 2 pm a freight train leaves a station and travels at 42 km/h. at 11pm and express train leaves the same station on a parallel track and travels at 105 km/h in the same direction. how far from the station will they meet?
since distance = speed 8 time, we want
42t = 105(t-9)
t = 15
So, at 5 am the next day they meet, after having gone 630km.
Or, you can consider that the freight train has a 9*42=378km head start, so the express train, traveling 63km faster, makes up the distance in 6 hours, after 630km.
how did you get 630km
multiply the speed by the time taken. The freight train traveled for 15 hours at 42 km/hr.
To find out how far from the station the two trains will meet, you need to determine the time it takes for them to meet.
First, let's find the time it takes for the trains to meet. We know that the first train leaves at 2 pm, and the second train leaves at 11 pm, which means there is a time difference of 9 hours between their departure times.
To find the time it takes for the trains to meet, we need to consider the relative speed at which they are traveling. The relative speed is the difference between the speeds of the two trains. In this case, the relative speed is 105 km/h (express train speed) - 42 km/h (freight train speed), which equals 63 km/h.
Now, we can use the formula: time = distance / speed.
Since we want to find the time it takes for the trains to meet, and we know the relative speed, we can rearrange the formula as: time = distance / relative speed.
Substituting the values we know, the time it takes for the trains to meet is: time = distance / 63 km/h.
Since the trains are moving in the same direction, the express train is effectively chasing the freight train. To find out where they meet, we multiply the time it takes for them to meet by the speed of the express train. This will give us the distance traveled by the express train when they meet.
So, distance = time * 105 km/h.
Substituting the calculated time value, distance = (distance / 63 km/h) * 105 km/h.
Simplifying, distance = (distance * 105 km/h) / 63 km/h.
To solve for distance, we can cross-multiply: distance * 63 km/h = distance * 105 km/h.
Now, we can cancel out the distance on both sides of the equation: 63 km/h = 105 km/h.
Simplifying further, we find that distance = 9 * 105 km / (105 km/h - 42 km/h).
Evaluating the expression, distance = 945 km / 63 km/h.
Therefore, the two trains will meet approximately 15 km from the station.