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

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by BTGmoderatorDC » Thu Nov 01, 2018 9:46 pm

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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

OA A

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by Jay@ManhattanReview » Thu Nov 01, 2018 11:20 pm
BTGmoderatorDC 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

OA A

Source: Manhattan Prep
Say the speed of Barry is x meters/second and the speed of the walkway is y meters/seconds

When moving along the walkway, the speed of Barry = (x + y) m/s
=> Length of the walkways (distance traveled) by Barry = (x + y)*30 meters

When moving in the opposite direction of the walkway, the speed of Barry = (x - y) m/s; x > y
=> Length of the walkways (distance traveled) by Barry = (x - y)*120 meters

=> (x + y)*30 = (x - y)*120

5y = 3x ---(1)

Again, length of the walkways (distance traveled) by Barry = 30 meters (given) = (x + y)*30

(x + y)*30 = 30

x + y = 1 ---(2)

From (1) and (2), we get x = 5/8 m/s

Time need to walk on walkway when walkway is not moving = Length/speed of Barry = 30/(5/8) = 48 seconds.

The correct answer: A

Hope this helps!

-Jay
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by GMATGuruNY » Fri Nov 02, 2018 3:27 am
BTGmoderatorDC 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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by swerve » Fri Nov 02, 2018 10:07 am
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.
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by deloitte247 » Sat Nov 03, 2018 2:51 pm
let barry's speed be b m/s
let barry walk way speed be w m/s
$$speed=\frac{dis\tan ce}{time}$$
$$b+w=\frac{30meters}{30\sec onds},\ where\ b+w=speed$$
b+w = 1m/s
so also
$$b-w=\frac{30metres}{120\sec onds},\ where\ b-w=speed$$
b - w =1/4 mls
$$speed\ of\ walking\ =\frac{1}{4}$$
$$sum\min g\ the\ two\ speed\ together$$
$$\left(b+w\right)+\left(b-w\right)=\frac{1}{1}+\frac{1}{4}$$
$$b+b=\frac{\left(4+1\right)}{4}$$
$$2b=\frac{5}{4}\ ;\ b=\frac{5}{8}$$
$$from\ speed=\frac{dis\tan ce}{time}$$
$$T=\frac{Dis\tan ce}{speed}$$ $$=\frac{30metres}{\frac{5}{8}}=6\cdot8=48$$
$$answer\ is\ Option\ A$$
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by Scott@TargetTestPrep » Sat Nov 03, 2018 4:56 pm
BTGmoderatorDC 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 = â…�

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 the rate of the walkway = w, Barry's rate = r and the length of the walkway = d.

Since it takes 30 seconds or 1/2 minutes 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: 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

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