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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 [#permalink]

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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
[Reveal] Spoiler: OA

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Re: Barry walks from one end to the other of a 30-meter long [#permalink]

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nitzz 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 Barry's speed be x m/s and walkway's speed by y m/s. We need to find 30/x.

If Barry walks in the direction of the moving walkway, the total speed is x + y. Time taken is 30/(x+y)
Thus, 30/(x+y) = 30

=> x + y = 1 ... (1)

If Barry walks against the moving walkway's direction, total speed is x-y. Time take is 30(x-y)
Thus, 30/(x-y) = 120

=> x - y = 1/4 ... (2)

Add (1) and (2),
=> 2x = 5/4
=> x = 5/8

therefore, 30/x = 48

Right answer is A.
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Re: Barry walks from one end to the other of a 30-meter long [#permalink]

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nitzz 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


Say Barry's speed is \(b\) meter per second and walkaway speed is \(w\) meter per second, then as \(Speed=\frac{Distance}{Time}\) we'll have that:

\(b+w=\frac{30}{30}=1\);
\(b-w=\frac{30}{120}=\frac{1}{4}\);

Sum these two equations; \(2b=\frac{5}{4}\) --> \(b=\frac{5}{8}\).

\(Time=\frac{Distance}{Speed}=\frac{30}{(\frac{5}{8})}=48\).

Answer: A.

Hope it helps.
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Re: Barry walks from one end to the other of a 30-meter long [#permalink]

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New post 09 Dec 2012, 20:54
How do we know that it is b-w? Why cant it be w-b. The question never says anything about the speeds of b or w individually.

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Re: Barry walks from one end to the other of a 30-meter long [#permalink]

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maddyboiler wrote:
How do we know that it is b-w? Why cant it be w-b. The question never says anything about the speeds of b or w individually.


If it is w-b, it means that speed of walkway is more than than his speed, then how will he reach the other end of the walkway.
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Re: Barry walks from one end to the other of a 30-meter long [#permalink]

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New post 10 Dec 2012, 05:41
Make sense, thanks.

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Re: Barry walks from one end to the other of a 30-meter long [#permalink]

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New post 31 Dec 2013, 09:03
nitzz 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



We have 30 (a+b) = 30
a+b = 1

We also get that 120 (a-b) = 30
So a-b = 1

So we have that a = 5/8

So 30*8/5 = 48

Answer is A

Hope it helps!
Cheers

J :)

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Re: Barry walks from one end to the other of a 30-meter long [#permalink]

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Let's try something else JFF ('Just for Fun')

B = Barry's Rate
W= Walkway's

So we have 30 (b+w) = 120 (b-w)
5w = 3b

D=30 (8/5b) = 48b

Time takes for Barry

t = D/R = 48b / b = 48 seconds

Answer: A

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Re: Barry walks from one end to the other of a 30-meter long [#permalink]

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New post 20 May 2014, 05:48
Do we actually need to know that the distance is 30 meters?

IF we learn that w=3b/5 we can find distance in terms of 'b' and then divide by rate 'b' to figure out that it will take Ben 48 seconds to reach the end of the walkway

Please advice
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Re: Barry walks from one end to the other of a 30-meter long [#permalink]

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New post 20 May 2014, 06:03
jlgdr wrote:
Do we actually need to know that the distance is 30 meters?

IF we learn that w=3b/5 we can find distance in terms of 'b' and then divide by rate 'b' to figure out that it will take Ben 48 seconds to reach the end of the walkway

Please advice
Cheers!
J


No we don't need this value of 30 meters since the distance remains the same while travelling up and down and thus, speeds are inversely proportional to the time taken. The information is superfluous.


Hope it helps!!!

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Barry walks from one end to the other of a 30-meter long [#permalink]

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New post 26 Jun 2016, 23:36
s1 = 30/30 = 1 metre/sec
s2 = 30/120 = 0.25 metres/sec
now
x+y=1
x-y=0.25
or,
2x=1.25 ==> x = 0.625 metres/sec
and y = 0.375 metres/sec
time taken by barry = 30000/625=48 sec

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Re: Barry walks from one end to the other of a 30-meter long [#permalink]

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New post 21 Nov 2016, 12:28
So basically since barry is moving at a rate and its given that walkway is also moving,thus speed of the walkway must be considered.Right?

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Re: Barry walks from one end to the other of a 30-meter long [#permalink]

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New post 07 Aug 2017, 07:59
Bunuel wrote:
nitzz 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


Say Barry's speed is \(b\) meter per second and walkaway speed is \(w\) meter per second, then as \(Speed=\frac{Distance}{Time}\) we'll have that:

\(b+w=\frac{30}{30}=1\);
\(b-w=\frac{30}{120}=\frac{1}{4}\);

Sum these two equations; \(2b=\frac{5}{4}\) --> \(b=\frac{5}{8}\).

\(Time=\frac{Distance}{Speed}=\frac{30}{(\frac{5}{8})}=48\).

Answer: A.

Hope it helps.


Hi Bunuel,
May I understand the thought process when you formed these 2 equations?
\(b+w=\frac{30}{30}=1\);
\(b-w=\frac{30}{120}=\frac{1}{4}\);

Thanks!

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Re: Barry walks from one end to the other of a 30-meter long [#permalink]

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New post 07 Aug 2017, 08:42
nitzz 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=B's speed
w=walkway speed
b+w=30 meters/30 sec=1 mps
b-w=30 meters/120 sec=1/4 mps
adding the two equations,
b=5/8 mps
30 meters/(5/8) mps=48 sec
A

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Re: Barry walks from one end to the other of a 30-meter long [#permalink]

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nitzz 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


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

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.

Answer: A
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Re: Barry walks from one end to the other of a 30-meter long   [#permalink] 10 Aug 2017, 09:29
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