A train leaves a station and travels north at a speed of 75mph. Two hours later, a second train leaves on a parallel track and travels north at 125mph. How far from the station will they meet?
The first train has a lead of 150 miles
The 2nd train catches up at a rate of 125-75 = 50 mi/hr
so, it will take 3 hours.
In that time, the 2nd train will have gone 375 miles
The first train will have gone 150+3*75 = 375 miles
distance = speed * time
speed 1 = 75
speed 2 = 125
time 1 = t
time 2 = t - 2
distances the same
75 t = 125 (t-2)
75 t = 125 t - 250
250 = 50 t
t = 5 hours
so what is 75 * 5 ?
To find out how far the two trains will meet, we can first calculate the distance the first train will have traveled in the two hours before the second train starts.
Distance = Speed * Time
So, the distance the first train will have traveled is:
Distance = 75mph * 2 hours = 150 miles
Now, let's consider the time it takes for the second train to catch up with the first train. Since both trains are traveling in the same direction, we can calculate the relative velocity between the two trains.
Relative Velocity = Speed of the first train - Speed of second train
Relative Velocity = 75mph - 125mph = -50mph
Now, let's calculate the time it takes for the second train to catch up with the first train by dividing the distance traveled by the relative velocity.
Time = Distance / Relative Velocity
Time = 150 miles / -50mph = -3 hours
Since we have a negative value for time, it means that the second train catches up with the first train 3 hours before the second train started. This indicates that the two trains meet 3 hours after the second train starts.
Now, let's calculate the distance from the station where the trains will meet.
Distance = Speed of second train * Time
Distance = 125mph * 3 hours = 375 miles
Therefore, the two trains will meet 375 miles from the station.