To do this you have to do two things, 1 establish the distance between the aircraft and then establish the closing speed.
Beside myself assumes that the flights are travelling at the same speed.
Here is an example that I hope I can explain without a drawing ( and my math is correct);
Airway segment - AAA to BBB. 360nm long
Aircraft 1 passes AAA at 1000 and estimates BBB at 1100
Aircraft 2 passes BBB at 1010 and estimates AAA at 1055
When will they pass?
1. Ask yourself where Aircraft 1 is when aircraft 2 passes BBB
Answer = 10 min after AAA.
2. With the estimates and known segment length you can work out using groundspeed how far Aircraft 1 has travelled in 10 minutes - 60nm in this example.
So when Aircraft 2 passes BBB, Aircraft 1 is 60nm past AAA or more importantly Aircraft 1 is (360-60)= 300nm from BBB
Thus at 1010 the aircraft are 300nm appart.
Based on estimates and segment length, Aircraft 1 has a groundspeed of 360Kt (6nm per minute) and Aircraft 2 has a groundspeed of 480Kt (8nm per minute).
Their closing speed is thus 14nm per minute.
At that closing speed and that distance appart they will cross inbetween 21 and 22 minutes (mental rather than calculator).
That means that the pass happens between 1031 and 1032.
Using 10 minutes before and after the estimated pass, gives you 1021 to 1042.
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You can crosscheck your calculations by asking yourself where each aircraft is at 1031
Aircraft 1 will be 31*6 = 186nm past AAA
Aircraft 2 will be 21*8 = 168nm past BBB.....which is 192 from AAA.
At 1031 the aircraft are 6nm appart closing at 14nm per minute!
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To sumarise, check where the first aircraft to enter the segment is when the second one enters and this gives you the distance appart. Use the estimates and known segment length to calculate the closing speed.
The distance the aircraft are appart when the second one enters the segment divided by the closing speed is the time to cross.
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You can use a similar for overtake.
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The above allows for different ground speeds of the aircraft and uses the info available from the FPS
Regards,
DFC