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

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

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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 OA=A.

Source: Manhattan GMAT.

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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
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.

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If s is his speed, and w the speed of the walkway, then when he walks with the walkway, his net speed is s+w, and when he walks against the walkway, his net speed is s-w.

Using the familiar S = D/T equation for both cases, we have:

s+w = 30/30 = 1
s-w = 30/120 = 1/4

and adding these two equations, so that the w disappears, we find s = 5/8. So we just want to know: how long does it take to walk 30 meters at a speed of 5/8 meters per second? Since T = D/S, the answer is 30 / (5/8) = 240/5 = 480/10 = 48 seconds.

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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 OA=A.

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 = ⅝

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.

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