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

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

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

Source: Manhattan Prep

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Source: Beat The GMAT — Problem Solving | Thu Nov 01, 2018 9:46 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

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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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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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swerve: Legendary Member; Posts: 2579; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

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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deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

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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Scott@TargetTestPrep: GMAT Instructor; Posts: 8211; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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 = 1Â¼

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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