Walking Way

[vinay1983]

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?

A.48
B.60
C.72
D.75
E.80

[Brent@GMATPrepNow]

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?

A.48
B.60
C.72
D.75
E.80

Let W = Speed of walkway in METERS per MINUTE
Let B = Barry's normal walking speed in METERS per MINUTE
So, B+W = Barry's net speed when he's walking WITH the walkway, and B-W = Barry's net speed when he's walking AGAINST the walkway.

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.
Traveling 30 meters in 30 seconds, is the same as traveling 60 meters in 60 seconds (i.e., 1 minute).
In other words, B+W = 60 meters per minute

...it takes Barry 120 seconds because he is traveling against the direction of the moving walkway.
Traveling 30 meters in 120 seconds, is the same as traveling 15 meters in 60 seconds (i.e., 1 minute).
In other words, B-W = 15 meters per minute

We have:
B + W = 60
B - W = 15
Add the two equations to get 2B = 75
Which means B = 75/2 = 37.5
In other words, Barry's normal walking speed is 37.5 meters per minute.

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? (a distance of 30 meters)
Time = distance/speed
= 30/37.5
STOP
Notice that 30/37.5 evaluates to be less than 1, which means it will take less than 1 minute for Barry to travel 30 meters.
Since only 1 answer choice is LESS THAN 1 minutes, the correct answer must be A

Cheers,
Brent

[theCodeToGMAT]

Distance = 30
Rate = B + W
T1= 30 sec
T2= 120 sec

Trip to End
s = d/t
B + W = 30/30

Return Trip
B - W = 30/120

B + W = 1
4B - 4W = 1
==> 4(1-W) - 4W = 1
==> 4 -8W = 1
==> W = 3/8
===> B = 5/8

Time without Walkway= 30/5/8 = 48
Answer [spoiler]{A}[/spoiler]

[GMATGuruNY]

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?

A.48
B.60
C.72
D.75
E.80

Let B = Barry's rate and W = the walkway's rate.
The distance can be ANY VALUE.
Let the distance = 240 meters.

WITH the walkway, the time = 30 seconds:
Here, Barry and the walkway WORK TOGETHER, so we ADD their rates:
B+W = d/t = 240/30 = 8 meters per second.

AGAINST the walkway, the time = 120 seconds:
Here, the walkway works AGAINST Barry, so we SUBTRACT their rates:
B-W = d/t = 240/120 = 2 meters per second.

Adding together B+W = 4 and B-W = 2, we get:
(B+W) + (B-W) = 8+2
2B = 10
B = 5 meters per second.

Time for Barry alone:
d/r = 240/5 = 48 seconds.

The correct answer is A.