Time And Distance Problem (II) (Posted on 2006-12-29)

P and Q are two stations 34 kilometres apart. Rick starts from P precisely at 12 noon and walks toward Q at the constant rate of 4 kilometres per hour. After journeying on for 3/2 hours he takes a rest for another 3/2 hours and then resumes his journey at the constant rate of 5 kilometres per hour.

Saul leaves Q exactly 2 hours after Rick leaves P and travels at a constant rate of 5 kilometres per hour for 2 hours. He (Saul) then takes rest for one hour before resuming his journey (towards P) at the constant rate of 4 kilometres per hour.

When and where will Rick and Saul meet? What was the distance between them at 3:00 PM? Determine when Rick and Saul were 8 kilometres apart for the first time.

Note: Rick and Saul keep on walking after they meet until they reach their respective destinations.