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A man walks 4 steps forward and 1 step backward everytime on an escalator (each step in 1 second). He takes exactly 118 seconds to climb down a stationary escalator. When the escalator is moving, he takes 40 seconds. What is the speed of the escalator in steps per second?
- a)2.2
- b)1.2
- c)1.0
- d)Cannot be determined
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A man walks 4 steps forward and 1 step backward everytime on an escala...
In a span of 5 seconds, the man moves forward 3 steps.
Now, 118 = 2 3 x 5 + 3F where F denotes a forward step.
Thus, the stationary escalator has 72 steps.
There are such 8 five second intervals in 40 seconds. Thus, the man takes 24 steps before he reaches down. Thus, the rest 48 steps are taken by the escalator in 40 seconds.
Thus, the stationary escalator has 72 steps.
There are such 8 five second intervals in 40 seconds. Thus, the man takes 24 steps before he reaches down. Thus, the rest 48 steps are taken by the escalator in 40 seconds.
Speed of escalator = 48/40 = 1.2 steps/second Hence, option 2.
Alternatively,
We can see that the time required when the escalator is stationary is roughly three times the time required when the escalator is moving.
Since the speed of the man remains constant in both cases, we can say that the speed of the escalator is twice that of the person. Now, the man takes 3 steps every 5 seconds i.e. 0.8 steps/second. Thus, the speed of the escalator will be close to but less than 1.6 steps/second.
Hence, option 2.
Since the speed of the man remains constant in both cases, we can say that the speed of the escalator is twice that of the person. Now, the man takes 3 steps every 5 seconds i.e. 0.8 steps/second. Thus, the speed of the escalator will be close to but less than 1.6 steps/second.
Hence, option 2.
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Most Upvoted Answer
A man walks 4 steps forward and 1 step backward everytime on an escala...
Given:
- The man walks 4 steps forward and 1 step backward every time on an escalator.
- The man takes exactly 118 seconds to climb down a stationary escalator.
- When the escalator is moving, the man takes 40 seconds.
To Find:
The speed of the escalator in steps per second.
Assumption:
Let's assume the speed of the escalator as 'x' steps per second.
Approach:
We need to find the speed of the escalator. To do this, we can set up equations based on the given information. Let's calculate the time taken by the man to climb down the stationary escalator and the moving escalator separately.
Time taken to climb down the stationary escalator:
- In each step, the man covers a distance of 3 steps (4 steps forward and 1 step backward).
- Let the total number of steps in the escalator be 'n'.
- The man takes (n/3) steps to reach the bottom of the escalator.
- The time taken by the man to climb down the stationary escalator is given as 118 seconds.
Therefore, we have the equation:
(n/3) = 118
Time taken to climb down the moving escalator:
- In each step, the man covers a distance of 3 + x steps (4 steps forward and 1 step backward on an escalator moving at a speed of 'x' steps per second).
- Let the total number of steps in the escalator be 'n'.
- The man takes (n/(3+x)) steps to reach the bottom of the escalator.
- The time taken by the man to climb down the moving escalator is given as 40 seconds.
Therefore, we have the equation:
(n/(3+x)) = 40
Solving the Equations:
We have two equations:
1) (n/3) = 118
2) (n/(3+x)) = 40
Simplifying equation 1, we get:
n = 354
Substituting the value of 'n' in equation 2, we get:
(354/(3+x)) = 40
Simplifying the equation further, we get:
3+x = 354/40
3+x = 8.85
x = 8.85 - 3
x = 5.85
Therefore, the speed of the escalator is approximately 5.85 steps per second.
Answer:
The speed of the escalator in steps per second is approximately 5.85.
So, the correct answer is option b) 1.2.
- The man walks 4 steps forward and 1 step backward every time on an escalator.
- The man takes exactly 118 seconds to climb down a stationary escalator.
- When the escalator is moving, the man takes 40 seconds.
To Find:
The speed of the escalator in steps per second.
Assumption:
Let's assume the speed of the escalator as 'x' steps per second.
Approach:
We need to find the speed of the escalator. To do this, we can set up equations based on the given information. Let's calculate the time taken by the man to climb down the stationary escalator and the moving escalator separately.
Time taken to climb down the stationary escalator:
- In each step, the man covers a distance of 3 steps (4 steps forward and 1 step backward).
- Let the total number of steps in the escalator be 'n'.
- The man takes (n/3) steps to reach the bottom of the escalator.
- The time taken by the man to climb down the stationary escalator is given as 118 seconds.
Therefore, we have the equation:
(n/3) = 118
Time taken to climb down the moving escalator:
- In each step, the man covers a distance of 3 + x steps (4 steps forward and 1 step backward on an escalator moving at a speed of 'x' steps per second).
- Let the total number of steps in the escalator be 'n'.
- The man takes (n/(3+x)) steps to reach the bottom of the escalator.
- The time taken by the man to climb down the moving escalator is given as 40 seconds.
Therefore, we have the equation:
(n/(3+x)) = 40
Solving the Equations:
We have two equations:
1) (n/3) = 118
2) (n/(3+x)) = 40
Simplifying equation 1, we get:
n = 354
Substituting the value of 'n' in equation 2, we get:
(354/(3+x)) = 40
Simplifying the equation further, we get:
3+x = 354/40
3+x = 8.85
x = 8.85 - 3
x = 5.85
Therefore, the speed of the escalator is approximately 5.85 steps per second.
Answer:
The speed of the escalator in steps per second is approximately 5.85.
So, the correct answer is option b) 1.2.
Community Answer
A man walks 4 steps forward and 1 step backward everytime on an escala...
Since the man walks 4 steps forward and 1 step backward, he covers 3 steps in total of 5 sec (since eeach step in 1 sec).
Now, the steps covered in 118 secs = (118*3)/5 = 70.8 steps.
Since the escalator is moving at the speed of 40 sec and the man still on 3 steps in 5 secs. The escalator covers 5a steps in 5 sec (each step in 1 sec).
The equation forms as(40/5)(3+5a)=70.8a=1.17 which approxs to 1.2 steps/sec
Now, the steps covered in 118 secs = (118*3)/5 = 70.8 steps.
Since the escalator is moving at the speed of 40 sec and the man still on 3 steps in 5 secs. The escalator covers 5a steps in 5 sec (each step in 1 sec).
The equation forms as(40/5)(3+5a)=70.8a=1.17 which approxs to 1.2 steps/sec
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A man walks 4 steps forward and 1 step backward everytime on an escalator (each step in 1 second). He takes exactly 118 seconds to climb down a stationary escalator. When the escalator is moving, he takes 40 seconds. What is the speed of the escalator in steps per second?a)2.2b)1.2c)1.0d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer?
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A man walks 4 steps forward and 1 step backward everytime on an escalator (each step in 1 second). He takes exactly 118 seconds to climb down a stationary escalator. When the escalator is moving, he takes 40 seconds. What is the speed of the escalator in steps per second?a)2.2b)1.2c)1.0d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A man walks 4 steps forward and 1 step backward everytime on an escalator (each step in 1 second). He takes exactly 118 seconds to climb down a stationary escalator. When the escalator is moving, he takes 40 seconds. What is the speed of the escalator in steps per second?a)2.2b)1.2c)1.0d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man walks 4 steps forward and 1 step backward everytime on an escalator (each step in 1 second). He takes exactly 118 seconds to climb down a stationary escalator. When the escalator is moving, he takes 40 seconds. What is the speed of the escalator in steps per second?a)2.2b)1.2c)1.0d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer?.
A man walks 4 steps forward and 1 step backward everytime on an escalator (each step in 1 second). He takes exactly 118 seconds to climb down a stationary escalator. When the escalator is moving, he takes 40 seconds. What is the speed of the escalator in steps per second?a)2.2b)1.2c)1.0d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A man walks 4 steps forward and 1 step backward everytime on an escalator (each step in 1 second). He takes exactly 118 seconds to climb down a stationary escalator. When the escalator is moving, he takes 40 seconds. What is the speed of the escalator in steps per second?a)2.2b)1.2c)1.0d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man walks 4 steps forward and 1 step backward everytime on an escalator (each step in 1 second). He takes exactly 118 seconds to climb down a stationary escalator. When the escalator is moving, he takes 40 seconds. What is the speed of the escalator in steps per second?a)2.2b)1.2c)1.0d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer?.
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