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 is A.
What are the calculus that I should do to solve this PS question?
Barry walks from one end to the other of a 30-meter
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Let B = Barry's rate and W = the walkway's rate.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 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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We can let the rate of the walkway = w and Barry's rate = r.Vincen 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
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 = â…�
Thus, if the walkway were not moving, it would take Barry 30/(5/8) = 240/5 = 48 seconds to walk its length.
Answer: A
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