Can some one please help me with this word problem? I`ve tried 3 times and can`t get it.?

Question

A southbound train leaves a station at 8am and a northbound train leaves the same station at 9 am. At 10 am the trains are 500km apart and at 11 am they are 850 km apart. Assuming constant speeds, how fast is each train travelling? I am having a real problem setting up a chart for this question.

Answer 1

S = southbound speed
N = northbound speed
d = distance
x = time from 8am
S(x) + N(x-1) = d

S*2 + N*1 = 500 => N = 500 - 2S
S*3 + N*2 = 850 = 3S + (1000 -4S) = 1000 - S
S = 150, N = 200

Answer 2

First, you need to draw a velocity-time graph where velocity is in km/h and time is in h(hour). Number the time axis with 0, 1, 2, 3. These mean 8am, 9am, 10am, and 11am respectively. The graph would be something like this: for the southbound train, draw a straight line below the time-axis and label V1 for y-intercept. For the northbound train, draw a straight line above the time-axis but the line starts at t=1 because the train leaves at 9am (i.e. t=1). Label V2 on the velocity-axis. Note: a straight line is drawn because both trains are at constant speed. Now, the area under the graph is the distance travelled. (A1) Area travelled by southbound train after 2 hours (at 10am from 8am) - (A2) Area travelled by north bound train after 1 hour (at 10am from 9am) = 500. When you shade the area under the line it would appear as a rectangle. So, A1 = 2V1 and A2 = V2. This implies 2V1 - V2 = 500 (equation1). Then, (A3) Area travelled by southbound train after 3 hours (at 11am from 8am) - (A4) Area travelled by north bound train after 2 hour (at 11am from 9am) = 850. So, A3 = 3V1 and A4 = 2V2. This implies 3V1 - 2V2 = 850 (equation2). Now we have 2 equations: 2V1 - V2 = 500 and 3V1 - 2V2 = 850. Solve them simultaneously and you would get (Southbound train) V1 = 150km/h and (Northbound train) V2 = -200km/h. You get a negative number for V2 because northbound train travels in the oppsite direction to southbound train.
(Hope this will help you.)

Answer 3

The only way this is possible is that the trains are going in opposite directions (Try and make them go the same direction, I dare you)

Assume that the 1st train goes x km/hr and the second goes y km/hr. Then x+y=350 (since they were 350 km further apart after one hour). Also, 3x+2y=850 (since they are 850 km apart 3 hours after the first one leaves.

Solve the system and x=150, y=200.

That means the first train goes 150 km/hr in one direction, with the second train going 200 km/hr in the opposite direction