Problem: Two horsemen at the same time started riding from A and B (one from each point) points, they rode with a constant velocity. When they arrived at any point, they immedeately turned around and rode back. First time they had met 40km from B, and second time, after 8h from the first meet up, they met at 20km from point A. Find the distance between A and B, and velocity of the horsemen.
My attempt to solve it:
x - distance between points A and b;
1st rider starts at A, 2nd - at B.
First, I noticed that there are 2 different possibilities for 2nd meet up. To be more concrete, 2 different possibilities for horsemen directions (hence, the distances each of them had traveled):
1) Both of their speeds were quite normal, so 2nd rider got to the point A and rode 20km until they had met. 1st rider got to the point B, then turned back and rode $x - 20$ km until they had met.
2) 2nd rider was very slow, so it managed to get only x - 40 - 20 km until 1st rider got to them. 1st rider in this case went to point B and turned back.
However, after I had noticed that the problem stopped me. I can describe their traveled distance or velocity, however, I can't figure exact numbers:
1st step) distance for 1st rider = x - 40; istance for 2nd rider = 40
2nd step 1st possibility) distance for 1st rider = x - 20 + 40 = x + 20; distance for 2nd rider = x - 40 + 20 = x - 20
2nd step 2nd possibility) distance for 1st rider = 20 + x - 40 = x - 20; distance for 2nd rider = x - 40 - 20 = x - 60
Am I doing everything good? What should I be doing next?