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?

I know that this question has been answered in previous posts, but I am just not able to grasp the logic behind it. Please look at my explanation below and guide me in the right direction.

I read through the explanation for the question above, but the place where I am stuck is


Bill would have to first "chase and catch up". Therefore, I envisioned the problem as follows:

Chase and catch + be with the group

To Chase and Catch:


When bill starts, the group is already 120 ft ahead of him, so first he would have to cover the 120ft and then also cover the additional distance that the group would cover in the mean time

Bill's speed = 6 ft/sec

Distance to be covered = 120 ft

Relative Speed (since he is chasing) = 6-3 = 3ft/sec

Time to cover 120 ft = 120/3 = 40 secs.

But in the 40 secs that it took Bill to cover 120 ft, the Group must have already covered some distance.

Therefore the distance covered by the group in 40 secs = 40 *3 ft/sec(speed of group)= 120 ft

From above we know that the time it will take Bill to cover the remaining 120ft = 40secs ( I still use the relative speed here, because Bill has not caught up to the group yet)

Therefore total time taken by Bill to cover 240 ft = 40+40= 80 secs. But something does not seem right here.

Your help is needed here


Thank you