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Moody takes 30 seconds to finish riding an escalator if he walks on it at his normal speed in the same direction. He takes 20 seconds to finish riding the escalator if he walks at twice his normal speed in the same direction. If Moody decides to stand still on the escalator, then the time, in seconds, needed to finish riding the escalator is
Correct answer is '60'. Can you explain this answer?
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Moody takes 30 seconds to finish riding an escalator if he walks on it...
Given Data
- Moody takes 30 seconds to finish riding an escalator if he walks on it at his normal speed in the same direction.
- Moody takes 20 seconds to finish riding the escalator if he walks at twice his normal speed in the same direction.
To find
- The time needed to finish riding the escalator if Moody decides to stand still on the escalator.
Approach
1. Let the speed of the escalator be 'x' units per second.
2. Let Moody's normal walking speed be 'v' units per second.
3. Moody's speed while walking at twice his normal speed will be '2v' units per second.
4. Using the formula "distance = speed × time", we can write the following equations:
When Moody walks at his normal speed:
- Distance covered by Moody = Speed of Moody (v) × Time taken by Moody (30 seconds)
- Distance covered by the escalator = Speed of the escalator (x) × Time taken by Moody (30 seconds)
- Total distance covered = Distance covered by Moody + Distance covered by the escalator
When Moody walks at twice his normal speed:
- Distance covered by Moody = Speed of Moody (2v) × Time taken by Moody (20 seconds)
- Distance covered by the escalator = Speed of the escalator (x) × Time taken by Moody (20 seconds)
- Total distance covered = Distance covered by Moody + Distance covered by the escalator
Equating the total distances covered in both cases, we can solve for 'x' to find the speed of the escalator.
The equation becomes:
Speed of Moody × Time taken by Moody + Speed of the escalator × Time taken by Moody = Speed of Moody × Time taken by Moody + Speed of the escalator × Time taken by Moody
Simplifying this equation, we get:
v × 30 + x × 30 = 2v × 20 + x × 20
Solving for 'x', we get:
x = v/3
Therefore, the speed of the escalator is v/3 units per second.
Since Moody decides to stand still on the escalator, his speed relative to the escalator is 0 units per second. Therefore, the time needed to finish riding the escalator while standing still is:
Time = Distance / Speed
= (Speed of the escalator) × (Time taken by Moody)
= (v/3) × 30
= 10v
Given that Moody takes 30 seconds to finish riding the escalator when he walks at his normal speed, we can substitute v = 30 into the equation:
Time = 10v
= 10 × 30
= 300 seconds
Therefore, the time needed to finish riding the escalator while standing still is 300 seconds or 5 minutes.
- Moody takes 30 seconds to finish riding an escalator if he walks on it at his normal speed in the same direction.
- Moody takes 20 seconds to finish riding the escalator if he walks at twice his normal speed in the same direction.
To find
- The time needed to finish riding the escalator if Moody decides to stand still on the escalator.
Approach
1. Let the speed of the escalator be 'x' units per second.
2. Let Moody's normal walking speed be 'v' units per second.
3. Moody's speed while walking at twice his normal speed will be '2v' units per second.
4. Using the formula "distance = speed × time", we can write the following equations:
When Moody walks at his normal speed:
- Distance covered by Moody = Speed of Moody (v) × Time taken by Moody (30 seconds)
- Distance covered by the escalator = Speed of the escalator (x) × Time taken by Moody (30 seconds)
- Total distance covered = Distance covered by Moody + Distance covered by the escalator
When Moody walks at twice his normal speed:
- Distance covered by Moody = Speed of Moody (2v) × Time taken by Moody (20 seconds)
- Distance covered by the escalator = Speed of the escalator (x) × Time taken by Moody (20 seconds)
- Total distance covered = Distance covered by Moody + Distance covered by the escalator
Equating the total distances covered in both cases, we can solve for 'x' to find the speed of the escalator.
The equation becomes:
Speed of Moody × Time taken by Moody + Speed of the escalator × Time taken by Moody = Speed of Moody × Time taken by Moody + Speed of the escalator × Time taken by Moody
Simplifying this equation, we get:
v × 30 + x × 30 = 2v × 20 + x × 20
Solving for 'x', we get:
x = v/3
Therefore, the speed of the escalator is v/3 units per second.
Since Moody decides to stand still on the escalator, his speed relative to the escalator is 0 units per second. Therefore, the time needed to finish riding the escalator while standing still is:
Time = Distance / Speed
= (Speed of the escalator) × (Time taken by Moody)
= (v/3) × 30
= 10v
Given that Moody takes 30 seconds to finish riding the escalator when he walks at his normal speed, we can substitute v = 30 into the equation:
Time = 10v
= 10 × 30
= 300 seconds
Therefore, the time needed to finish riding the escalator while standing still is 300 seconds or 5 minutes.
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Moody takes 30 seconds to finish riding an escalator if he walks on it at his normal speed inthe same direction. He takes 20 seconds to finish riding the escalator if he walks at twice his normal speed in the same direction. If Moody decides to stand still on the escalator, then the time, in seconds, needed to finish riding the escalator isCorrect answer is '60'. Can you explain this answer?
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Moody takes 30 seconds to finish riding an escalator if he walks on it at his normal speed inthe same direction. He takes 20 seconds to finish riding the escalator if he walks at twice his normal speed in the same direction. If Moody decides to stand still on the escalator, then the time, in seconds, needed to finish riding the escalator isCorrect answer is '60'. 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 Moody takes 30 seconds to finish riding an escalator if he walks on it at his normal speed inthe same direction. He takes 20 seconds to finish riding the escalator if he walks at twice his normal speed in the same direction. If Moody decides to stand still on the escalator, then the time, in seconds, needed to finish riding the escalator isCorrect answer is '60'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Moody takes 30 seconds to finish riding an escalator if he walks on it at his normal speed inthe same direction. He takes 20 seconds to finish riding the escalator if he walks at twice his normal speed in the same direction. If Moody decides to stand still on the escalator, then the time, in seconds, needed to finish riding the escalator isCorrect answer is '60'. Can you explain this answer?.
Moody takes 30 seconds to finish riding an escalator if he walks on it at his normal speed inthe same direction. He takes 20 seconds to finish riding the escalator if he walks at twice his normal speed in the same direction. If Moody decides to stand still on the escalator, then the time, in seconds, needed to finish riding the escalator isCorrect answer is '60'. 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 Moody takes 30 seconds to finish riding an escalator if he walks on it at his normal speed inthe same direction. He takes 20 seconds to finish riding the escalator if he walks at twice his normal speed in the same direction. If Moody decides to stand still on the escalator, then the time, in seconds, needed to finish riding the escalator isCorrect answer is '60'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Moody takes 30 seconds to finish riding an escalator if he walks on it at his normal speed inthe same direction. He takes 20 seconds to finish riding the escalator if he walks at twice his normal speed in the same direction. If Moody decides to stand still on the escalator, then the time, in seconds, needed to finish riding the escalator isCorrect answer is '60'. Can you explain this answer?.
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