The Moving Walkway Question

[q1w2e3r4t5]

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[RonPurewal]

hi -

this problem has caused a great deal of anguish. for the record, it is probably a bit too complicated for the gmat; i don't think that the gmat will test things like speed relative to ground vs. speed relative to a moving frame of reference.

*** My question: In the first part of the explanation we subtract 3 ft from Bills combined rate of movement of 6 ft/sec because we are measuring just "Bills movement." Thus we get a speed of 3 feet per second for the first 240 feet because 6-3=3

imagine placing one still camera on the ground ("ground camera"), and placing another on the belt ("belt camera").

in the first part, the ground camera would record bill as moving 6 ft/sec, while the belt camera would record him as moving 3 ft/sec.

In the second part Bill is standing still with the group while the walkway is moving 3 feet per second. So why do we say that Bill covered the remaining 60 feet at 3 feet per second if we are just measuring Bills movement?

in the second part, the ground camera would record bill as moving 3 ft/sec, while the belt camera would record him as moving 0 ft/sec.


does that help?

[q1w2e3r4t5]

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[rchitta]

Relative speeds are always tricky. Unless specified or explicitly asked for you measure speeds with respect to something that is still.

Even though the belt is moving at 3ft/s, its irrelevant. What is Bill's rate of movement? (his speed + the speed of the belt) with respect to something that is static. 6ft/s

answer = 300/(240/6 + 60/3) = 5ft/s (which you already know :)) (Important to note that all the speeds here are speed at which Bill is moving with respect to the ground, 6ft/s and 3ft/s respectively)

Let's consider your point of treating the speeds with respect to the belt. If you ignore the belt speed then only bill is moving and no one else.

This means, distance between everyone and bill is only 120 ft and once Bill moves at 3ft/s and joins the other people no one else will move. Everyone stays still at the 120ft mark which seems kind of bogus. isn't it? :)

But it is mentioned in the problem that, Bill is moving towards the end of the walkway, so he has a speed and that is same as the speed of the walkway...for the rest of the distance.

[Ben Ku]

Thanks rchitta for the beautiful response!