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Bob can finish a job in 40 days, if he works alone. Alex is twice as fast as Bob and thrice as fast as Cole in the same job. Suppose Alex and Bob work together on the first day, Bob and Cole work together on the second day, Cole and Alex work together on the third day, and then, they continue the work by repeating this three-day roster, with Alex and Bob working together on the fourth day, and so on. Then, the total number of days Alex would have worked when the job gets finished, is
Correct answer is '11'. Can you explain this answer?
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Bob can finish a job in 40 days, if he works alone. Alex is twice as f...
Problem Analysis:
Let's analyze the given information:
- Bob can finish the job in 40 days if he works alone. This means that Bob's work rate is 1/40th of the job per day.
- Alex is twice as fast as Bob. This means that Alex's work rate is twice that of Bob, which is 1/20th of the job per day.
- Alex is thrice as fast as Cole. This means that Cole's work rate is 1/3rd of Alex's work rate, which is 1/60th of the job per day.
Approach:
To find the total number of days Alex would have worked when the job gets finished, we need to find the pattern of their work rotation and calculate the number of days Alex works in each cycle. We will then multiply this by the number of cycles it takes to complete the job.
Solution:
Let's break down the work rotation into cycles:
Cycle 1:
- Day 1: Alex and Bob work together.
- Day 2: Bob and Cole work together.
- Day 3: Cole and Alex work together.
In this cycle, Alex works on Day 1 and Day 3. So, in Cycle 1, Alex works for 2 out of 3 days.
Cycle 2:
- Day 4: Alex and Bob work together.
- Day 5: Bob and Cole work together.
- Day 6: Cole and Alex work together.
In this cycle, Alex works on Day 4 and Day 6. So, in Cycle 2, Alex works for 2 out of 3 days.
Cycle 3:
- Day 7: Alex and Bob work together.
- Day 8: Bob and Cole work together.
- Day 9: Cole and Alex work together.
In this cycle, Alex works on Day 7 and Day 9. So, in Cycle 3, Alex works for 2 out of 3 days.
From the pattern, we can observe that Alex works for 2 out of 3 days in each cycle.
Now, let's calculate the number of cycles it takes to complete the job:
- In each cycle, there are 3 days, and Alex works for 2 out of 3 days.
- So, the work completed by Alex in each cycle is (2/3) * 1/20 = 1/30th of the job.
To complete the job, Bob needs 40 days, which means he completes 1/40th of the job per day.
- So, in 1 day, Bob completes 1/40th of the job.
- In 3 days (1 cycle), Bob completes 3/40th of the job.
To find the number of cycles it takes to complete the job, we divide 1 by 3/40:
1 / (3/40) = 40/3
Since the number of cycles must be a whole number, we round up to the nearest whole number:
40/3 ≈ 13.33 (rounded up to 14)
Therefore, it takes 14 cycles to complete the job.
Finally, let's calculate the total number of days Alex would have worked:
- In each cycle, Alex works for 2 out of 3 days.
-
Let's analyze the given information:
- Bob can finish the job in 40 days if he works alone. This means that Bob's work rate is 1/40th of the job per day.
- Alex is twice as fast as Bob. This means that Alex's work rate is twice that of Bob, which is 1/20th of the job per day.
- Alex is thrice as fast as Cole. This means that Cole's work rate is 1/3rd of Alex's work rate, which is 1/60th of the job per day.
Approach:
To find the total number of days Alex would have worked when the job gets finished, we need to find the pattern of their work rotation and calculate the number of days Alex works in each cycle. We will then multiply this by the number of cycles it takes to complete the job.
Solution:
Let's break down the work rotation into cycles:
Cycle 1:
- Day 1: Alex and Bob work together.
- Day 2: Bob and Cole work together.
- Day 3: Cole and Alex work together.
In this cycle, Alex works on Day 1 and Day 3. So, in Cycle 1, Alex works for 2 out of 3 days.
Cycle 2:
- Day 4: Alex and Bob work together.
- Day 5: Bob and Cole work together.
- Day 6: Cole and Alex work together.
In this cycle, Alex works on Day 4 and Day 6. So, in Cycle 2, Alex works for 2 out of 3 days.
Cycle 3:
- Day 7: Alex and Bob work together.
- Day 8: Bob and Cole work together.
- Day 9: Cole and Alex work together.
In this cycle, Alex works on Day 7 and Day 9. So, in Cycle 3, Alex works for 2 out of 3 days.
From the pattern, we can observe that Alex works for 2 out of 3 days in each cycle.
Now, let's calculate the number of cycles it takes to complete the job:
- In each cycle, there are 3 days, and Alex works for 2 out of 3 days.
- So, the work completed by Alex in each cycle is (2/3) * 1/20 = 1/30th of the job.
To complete the job, Bob needs 40 days, which means he completes 1/40th of the job per day.
- So, in 1 day, Bob completes 1/40th of the job.
- In 3 days (1 cycle), Bob completes 3/40th of the job.
To find the number of cycles it takes to complete the job, we divide 1 by 3/40:
1 / (3/40) = 40/3
Since the number of cycles must be a whole number, we round up to the nearest whole number:
40/3 ≈ 13.33 (rounded up to 14)
Therefore, it takes 14 cycles to complete the job.
Finally, let's calculate the total number of days Alex would have worked:
- In each cycle, Alex works for 2 out of 3 days.
-
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Bob can finish a job in 40 days, if he works alone. Alex is twice as fast as Bob and thrice as fast as Cole in the same job. Suppose Alex and Bob work together on the first day, Bob and Cole work together on the second day, Cole and Alex work together on the third day, and then, they continue the work by repeating this three-day roster, with Alex and Bob working together on the fourth day, and so on. Then, the total number of days Alex would have worked when the job gets finished, isCorrect answer is '11'. Can you explain this answer?
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Bob can finish a job in 40 days, if he works alone. Alex is twice as fast as Bob and thrice as fast as Cole in the same job. Suppose Alex and Bob work together on the first day, Bob and Cole work together on the second day, Cole and Alex work together on the third day, and then, they continue the work by repeating this three-day roster, with Alex and Bob working together on the fourth day, and so on. Then, the total number of days Alex would have worked when the job gets finished, isCorrect answer is '11'. 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 Bob can finish a job in 40 days, if he works alone. Alex is twice as fast as Bob and thrice as fast as Cole in the same job. Suppose Alex and Bob work together on the first day, Bob and Cole work together on the second day, Cole and Alex work together on the third day, and then, they continue the work by repeating this three-day roster, with Alex and Bob working together on the fourth day, and so on. Then, the total number of days Alex would have worked when the job gets finished, isCorrect answer is '11'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Bob can finish a job in 40 days, if he works alone. Alex is twice as fast as Bob and thrice as fast as Cole in the same job. Suppose Alex and Bob work together on the first day, Bob and Cole work together on the second day, Cole and Alex work together on the third day, and then, they continue the work by repeating this three-day roster, with Alex and Bob working together on the fourth day, and so on. Then, the total number of days Alex would have worked when the job gets finished, isCorrect answer is '11'. Can you explain this answer?.
Bob can finish a job in 40 days, if he works alone. Alex is twice as fast as Bob and thrice as fast as Cole in the same job. Suppose Alex and Bob work together on the first day, Bob and Cole work together on the second day, Cole and Alex work together on the third day, and then, they continue the work by repeating this three-day roster, with Alex and Bob working together on the fourth day, and so on. Then, the total number of days Alex would have worked when the job gets finished, isCorrect answer is '11'. 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 Bob can finish a job in 40 days, if he works alone. Alex is twice as fast as Bob and thrice as fast as Cole in the same job. Suppose Alex and Bob work together on the first day, Bob and Cole work together on the second day, Cole and Alex work together on the third day, and then, they continue the work by repeating this three-day roster, with Alex and Bob working together on the fourth day, and so on. Then, the total number of days Alex would have worked when the job gets finished, isCorrect answer is '11'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Bob can finish a job in 40 days, if he works alone. Alex is twice as fast as Bob and thrice as fast as Cole in the same job. Suppose Alex and Bob work together on the first day, Bob and Cole work together on the second day, Cole and Alex work together on the third day, and then, they continue the work by repeating this three-day roster, with Alex and Bob working together on the fourth day, and so on. Then, the total number of days Alex would have worked when the job gets finished, isCorrect answer is '11'. Can you explain this answer?.
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