moving walk

[adam15]

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

[Stuart@KaplanGMAT]

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

[adam15]

Thank you Stuart for your prompt reply you said that "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," I think the group is moving as well with rate equal to 3f/s; so bill need to catch up the group first in order to stop. so we need to solve some equation that looks like the following
6t-120=-3t+240.
Thank you for you answer

[Stuart@KaplanGMAT]

Thank you Stuart for your prompt reply you said that "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," I think the group is moving as well with rate equal to 3f/s; so bill need to catch up the group first in order to stop. so we need to solve some equation that looks like the following
6t-120=-3t+240.
Thank you for you answer

Hi again!

Bill's total speed relative to the ground while he's walking is 6 f/s.

However, that other group is also on the moving walkway, so their speed relative to the ground is 3 f/s.

So, Bill's speed relative to that group is 6 f/s - 3 f/s = 3 f/s.

Here's the general rule for speed questions with multiple moving objects:

if the objects are moving in opposite directions (directly toward or away from each other): ADD the speeds; and

if the objects are moving in the same direction: SUBTRACT the speeds.

[adam15]

Thank you very much for your help, I got it finally

[vivekjaiswal]

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

There's another way we can solve this.
We understand that Bill stays on the walkway(walking on it, or standing with the group) as long as the group thats standing on the walkway stays on the walkway. And then he gets off the walkway with the group.
The group stays on the walkway for (300-120)/3 = 180/3 = 60s
Now Bill's avg speed should be 300/60 = 5fps

Hope this helps.