For each of the following questions, show your work algebraically. 1) Albus starts at an initial position of 0 m, and Chandra starts at an initial position of 75 m. If Albus moves towards Chandra at a rate of 4 m/s and Chandra moves towards Albus at a rate of 8 m/s, at what time and position will they meet each other? 2) Tim starts 50 m ahead of Radagast. Tim 'runs' forward at a rate of 0.1 m/s and Radagast also runs forward, but at a rate of 15 m/s. When and where does Radagast catch up to Tim? 3) Two rams start 20 m apart. If one ram runs 2.5 times as fast as the second ram, at what position will they collide? If the collision happens after 2 seconds, what are the velocities of the two rams? 4) Two rams start 20 m apart. If one ram runs z times as fast as the second ram, where z is any positive, real number, at what position will they collide? Your answer should be in terms of z. 5) A train leaves Cairo at 3:00 am, averaging 30 mph. Another train headed in the same direction leaves Cairo at 6:00 am, averaging 60 mph. To the nearest tenth, how many hours after the second train leaves will it overtake the first train? Where will this occur? 6) A train leaves Austin for Bogota at 2:15 am, averaging 80 mph. Another train leaves Bogota for Austin at 3:30 am, averaging 110 mph. If Bogota is 2855 miles from Austin, to the nearest minute, at what time will the two trains pass each other? Where will they pass each other? 7) SLIGHTLY UNRELATED CHALLENGE: You and your friend are going to race. For the race, you and your friend will run a distance d, turn around and return to where you started (for a total distance of 2d). You and your friend are equally fast, and run with a constant velocity v. However, when performing the race, your friend will be running on a moving sidewalk. So your friend will be helped by the moving sidewalk going one way, but slowed by the moving sidewalk going the other way. The moving sidewalk moves with a velocity relative to the ground of u. Who will win the race? You or your friend