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.

At 3pm Rick is 6km from P and Saul is 29km from P. So they are 23km apart. At 5pm Rick is 16km from P and Saul is 24km from P so they are 8km apart. At 6pm Rick is 21km from P and Saul is 20km from P so they met between 5 and 6pm. During this hour Rick traveled 5kph in t hours for a distance k while Saul traveled 4kph in t hours for a distance (8-k). Solving simultaneously for t, yields t=8/9 of an hour. So they met 8/9 of an hour after 5pm (5:53+1/3) at a distance of 20+4/9 km from P. 

Posted by Dennis on 2006-12-29 10:02:33