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A man moving upward on a staircase at the speed of x steps per second
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24 Apr 2023, 05:19
24 Apr 2023, 05:19
Expert Reply
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Question Stats:
91% (00:53) correct
8% (02:54) wrong based on 12 sessions
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A man moving upward on a staircase at the speed of x steps per second and takes a total of y seconds to reach to the top. At what speed he should walk to reach at the top in y/3 seconds ? (in steps per second)
A. 3/x
B. x/2
C. 3x/2
D. 2x
E. 3x
A. 3/x
B. x/2
C. 3x/2
D. 2x
E. 3x
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1053
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Re: A man moving upward on a staircase at the speed of x steps per second
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03 May 2023, 08:39
03 May 2023, 08:39
1
Expert Reply
Let's assume that the height of the staircase is h, and the number of steps is n. Therefore, the height of each step is h/n.
The time taken by the man to reach the top of the staircase is y seconds. Therefore, the total number of steps he takes is n, and the speed at which he is climbing the stairs is x steps/second. Therefore, we can write:
n = x*y -----(1)
Now, we need to find the speed at which he should walk to reach the top in y/3 seconds. Let's assume that he takes z steps/second while climbing the stairs.
The total number of steps he will take to reach the top in y/3 seconds can be calculated as:
n' = z*(y/3)
Since the number of steps remains the same, we can equate n and n' to get:
xy = z(y/3)
Simplifying the above equation, we get:
z = 3x
Therefore, the man should walk at a speed of 3x steps/second to reach the top in y/3 seconds.
Hence, the correct option is (E) 3x.
The time taken by the man to reach the top of the staircase is y seconds. Therefore, the total number of steps he takes is n, and the speed at which he is climbing the stairs is x steps/second. Therefore, we can write:
n = x*y -----(1)
Now, we need to find the speed at which he should walk to reach the top in y/3 seconds. Let's assume that he takes z steps/second while climbing the stairs.
The total number of steps he will take to reach the top in y/3 seconds can be calculated as:
n' = z*(y/3)
Since the number of steps remains the same, we can equate n and n' to get:
xy = z(y/3)
Simplifying the above equation, we get:
z = 3x
Therefore, the man should walk at a speed of 3x steps/second to reach the top in y/3 seconds.
Hence, the correct option is (E) 3x.
gmatclubot
Re: A man moving upward on a staircase at the speed of x steps per second [#permalink]
03 May 2023, 08:39
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