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# The ‘moving walkway’ is a 300-foot long walkway consisting of a convey

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Manager
Joined: 07 Jun 2015
Posts: 75
WE: Design (Aerospace and Defense)
Re: The ‘moving walkway’ is a 300-foot long walkway consisting of a convey  [#permalink]

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24 Jan 2016, 11:25
average speed = total distance covered by bill/ total time taken.

total distance covered by bill=300

total distance covered by those people in-front of him=300-120=180

total time taken by bill=total time taken by those people in-front of him=(300-120)/3=60sec ( since they move at const speed)

so avg speed of bill=300/60=5ft/sec
Manager
Joined: 20 Mar 2015
Posts: 60
Re: The ‘moving walkway’ is a 300-foot long walkway consisting of a convey  [#permalink]

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19 May 2016, 22:21
VeritasPrepKarishma wrote:
Gmatter111 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?

A. 2 feet per second
B. 2.5 feet per second
C. 3 feet per second
D. 4 feet per second
E. 5 feet per second

Using relative speed concepts:

Bill covers 120 feet at a relative speed of 6 - 3 = 3 feet/sec. Time taken to cover 120 feet = 120/3 = 40 sec
Distance covered in 40 secs = 6*40 = 240 feet
So now he just has 300 - 240 = 60 feet leftover to cover at 3 feet/sec
Time taken to cover 60 feet = 60/3 = 20 sec

Average Speed = Total Distance/Total Time = 300/(40 + 20) = 5 feet/sec

Bill and the group start at 180 feet.
Time taken to meet = initial distance/difference of speeds
$$\frac{180}{6-3}$$ = 60 sec

What I assumed here is that in this 60 sec Bill will complete the 300 distance.
Thus, I divided the total distance by total time.
=$$\frac{300}{60}$$
=5ft/sec

What, that I am assuming, is wrong? Is the way I got the answer wrong?
Intern
Joined: 27 Sep 2015
Posts: 5
Re: The ‘moving walkway’ is a 300-foot long walkway consisting of a convey  [#permalink]

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02 Oct 2017, 08:26
prome2 wrote:
Here's what I think the answer should be
-------

Time Bill takes to catchup with group = 120/3
= 40 secs
Time Group has moved in 40 secs = 40 x 3
= 120 feet
Remaining Distance on walkway = 300 - 120 -120
= 60
Time taken to cover the last 60 ft = 60/3
= 20sec

Total time Bill spends on walkway = 40 + 20 = 60 secs
Total length of walkway = 300 feet

Bill's Average speed = 300/60 = 5 ft/sec

This problem may also be solved with a shortcut. Consider that Bill’s journey will end when the crowd reaches the end of the walkway (as long as he catches up with the crowd before the walkway ends). When he steps on the walkway, the crowd is 180 feet from the end. The walkway travels this distance in (180 feet)/(3 feet per second) = 60 seconds, and Bill’s average rate of movement is (300 feet)/(60 seconds) = 5 feet per second
Intern
Joined: 20 Apr 2014
Posts: 2
Re: The ‘moving walkway’ is a 300-foot long walkway consisting of a convey  [#permalink]

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08 Sep 2018, 04:05
After going through all explanations given in this thread, I was way too confused why the relative speed of Bill is (6-3) 3 feet/sec. Since both Bill and group of people are moving on 3 feet/sec conveyor Belt, 3 feet/sec gets cancelled when Bill moves to catch up the group of people. Below is my explanation of my understanding.

The rate at which Bill moves is (6+3) 9 feet/sec.

The rate at which the group of people moves is 3 feet/sec.

The distance between Bill and group of people is 120 feet.

Since Bill and group of people are moving in same direction, the relative speed will be (9-3) 6 feet/sec
Total Time taken by Bill to cover 120 feet distance is 120/6 = 20 sec.

When Bill makes his move to catch up the group of people, even the group of people moves at 3 feet/sec. Total distance covered by Bill in 20 sec with his rate of 9 feet/sec is 180 feet, that makes remaining distance = 120 feet.

After Bill catches up with group of people he continues at a rate of 3 feet/sec, and time taken to cover that 120 feet at 3 feet/sec will be 40 sec.

Average rate of Bill = Total distance/Total Time = 300/60 = 5 feet/sec.
Re: The ‘moving walkway’ is a 300-foot long walkway consisting of a convey &nbs [#permalink] 08 Sep 2018, 04:05

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