Barry walks from one end to the other of a 30-meter long...

[MaysaJ757]

Hi,

I have a quick question about this problem:

Barry walks from one end to the other of a 30-meter long moving walkway at a constant rate in 30 seconds, assisted by the walkway. When he reaches the end, he reverses direction and continues walking with the same speed, but this time it takes him 120 seconds because he is traveling against the direction of the moving walkway. If the walkway were to stop moving, how many seconds would it take Barry to walk from one end of the walkway to the other?
(answer choices: 48, 60, 72, 75, 80, CAT 4 Quant #16)

How come you can't posit that since Barry walks from one end to the other in 30 seconds and the walkway is 30 meters long, that the combination of his rate and the walkway's rate is 1m/s? And then, couldn't you also calculate that if it takes him 120 seconds to cross 30 seconds when the walkway is AGAINST his direction, then "Barry minus walkway" equals 0.25m/s? I'm not necessarily clear on what to DO with that information but that's the road I took when I first attacked the problem. It seems strange that they give you both distance and time and you aren't supposed to calculate rate when that's what you would normally do when given this type of information.

Thanks,
M

[RonPurewal]

you can absolutely do the problem that way.
b + w = 1
b – w = 1/4
(b = barry's speed in m/s, w = speed of walkway in m/s)

thus b = 5/8 m/s, and so he would traverse the distance unassisted in 30/(5/8) = 48 seconds.

does the answer key not do this?

[RonPurewal]

if you have a certain amount of intuition about these things, you can also solve the problem with common-sense interpretation.

if barry needed 60 seconds to traverse the distance by himself, then the assisted time of 30 seconds would represent twice barry's unassisted speed.
if that's the case, then the walkway is just as fast as barry—and so barry would never traverse any distance against the walkway! it would move backward exactly as fast as barry would walk forward; in other words, it would become a treadmill.

... and for the answer choices larger than 60 seconds, barry is even slower than the walkway, so, if he tried to walk against it, he would travel backward.

so, 48 seconds is the only answer choice that actually allows barry to cover any distance while walking against the mechanism.

[RonPurewal]

and, there's already a thread on this problem:
https://www.manhattanprep.com/gmat/foru ... 19260.html

if there are any remaining issues, please post in the existing thread (which, incidentally, already contains an answer to the original question in this thread—there's much treasure to be found by searching the forum, ladies and gentlemen). thanks.