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

VJesus12 wrote: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

The [spoiler]OA=A[/spoiler].

We can let the rate of the walkway = w and Barry’s rate = r, both in meters per second.

Since he walks from one end to the other of a 30-meter moving walkway at a constant rate in 30 seconds, assisted by the walkway:

w + r = 30/30

w + r = 1

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:

r - w = 30/120

r - w = 1/4

Adding the two equations together, we have:

2r = 1¼

2r = 5/4

r = (5/4)/2 = �

Thus, if the walkway were not moving, it would take Barry 30/(5/8) = 240/5 = 48 seconds to walk its length.

Alternate Solution:

We can let w = the rate of the walkway, r = Barry’s rate, and d = the length of the walkway.

Since it takes 30 seconds, or 1/2 minute, for Barry to walk assisted by the walkway, we have d/(r + w) = 1/2.

Since it takes 120 seconds, or 2 minutes, for Barry to walk against the walkway, we have d/(r - w) = 2.

Let’s rewrite the first equation as d = r/2 + w/2 and then, multiply each side by 4 to obtain: 4d = 2r + 2w.

Notice that the second equation is equivalent to d = 2r - 2w. If we add the two equations together, we obtain 5d = 4r or, equivalently, d/r = 4/5 minutes. Notice also that d/r is the time required for Barry to walk the distance from one end of the walkway to the other end; therefore, it would take Barry 4/5 x 60 = 48 seconds to walk this length.

Answer: A


Source: Manhattan GMAT.