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Intern  Status: Apps time!
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Barry walks from one end to the other of a 30-meter long  [#permalink]

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26 00:00

Difficulty:   65% (hard)

Question Stats: 67% (02:44) correct 33% (02:45) wrong based on 624 sessions

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 58313
Re: Barry walks from one end to the other of a 30-meter long  [#permalink]

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6
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; $$2b=\frac{5}{4}$$ --> $$b=\frac{5}{8}$$.

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

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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8
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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3
3
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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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.
Intern  Joined: 31 Oct 2012
Posts: 21
Re: Barry walks from one end to the other of a 30-meter long  [#permalink]

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Make sense, thanks.
SVP  Joined: 06 Sep 2013
Posts: 1573
Concentration: Finance
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 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

Hope it helps!
Cheers

J SVP  Joined: 06 Sep 2013
Posts: 1573
Concentration: Finance
Re: Barry walks from one end to the other of a 30-meter long  [#permalink]

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1
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

SVP  Joined: 06 Sep 2013
Posts: 1573
Concentration: Finance
Re: Barry walks from one end to the other of a 30-meter long  [#permalink]

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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

Cheers!
J
Intern  Joined: 17 May 2014
Posts: 37
Re: Barry walks from one end to the other of a 30-meter long  [#permalink]

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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

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!!!
Director  G
Joined: 20 Feb 2015
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Concentration: Strategy, General Management
Barry walks from one end to the other of a 30-meter long  [#permalink]

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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
Intern  Joined: 16 Jul 2015
Posts: 35
GMAT 1: 580 Q37 V33 GMAT 2: 580 Q39 V31 GMAT 3: 560 Q40 V28 GMAT 4: 580 Q37 V32 GMAT 5: 680 Q45 V37 GMAT 6: 690 Q47 V37 Re: Barry walks from one end to the other of a 30-meter long  [#permalink]

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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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Joined: 18 Apr 2013
Posts: 33
Re: Barry walks from one end to the other of a 30-meter long  [#permalink]

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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; $$2b=\frac{5}{4}$$ --> $$b=\frac{5}{8}$$.

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

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!
VP  P
Joined: 07 Dec 2014
Posts: 1223
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 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
Target Test Prep Representative D
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Re: Barry walks from one end to the other of a 30-meter long  [#permalink]

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1
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.

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_________________ Re: Barry walks from one end to the other of a 30-meter long   [#permalink] 26 Aug 2018, 03:33
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