adam15 wrote:The 'moving walkway' is a 300-foot long walkway consisting of a conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a rate of 3 feet per second. Once Bill reaches the group of people, he stops walking and stands with them until the walkway ends. What is Bill's average rate of movement for his trip along the moving walkway?
2 feet per second
2.5 feet per second
3 feet per second
4 feet per second
5 feet per second
We need to divide Bill's journey into two parts: walking and standing still.
When Bill is walking, his rate = 3 f/s + 3 f/s = 6 f/s
When Bill is standing, his rate = 3 f/s
Taking a quick peek at the choices (always a good plan), we can already eliminate a, b and c; we know his average rate will be somewhere between 3 f/s and 6 f/s.
Next we need to determine how long each part of the journey takes.
While Bill is walking and the other group is standing, Bill's relative speed is 3 f/s. His distance to cover is 120 feet, so:
t = d/r = 120/3 = 40s
Now, during that 40s, Bill covers 6 * 40 = 240 feet (remember, his rate relative to the ground during this period is 6 f/s).
Since the entire walkway is 300 feet long, he still has 60 feet to cover.
t = d/r = 60/3 = 20s
So: total d = 300; total t = 40 + 20 = 60s
Therefore, average rate is:
total d/total t = 300/60 = 5 f/s... choose E
