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Working together, Jose and Jane can complete an assigned task in 20 days. However, if Jose worked alone and completed half the work and then Jane takes over and completes the second half, the task will be completed in 45 days. How long will Jose take to complete the task if he worked alone? Assume that Jane is more efficient than Jose.
- a)25 days
- b)30 days
- c)60 days
- d)65 days
- e)36 days
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Working together, Jose and Jane can complete an assigned task in 20 da...
Step 1: Assign Variables and Frame Equations
Let Jose take 'x' days to complete the task if he worked alone.
Let Jane take 'y' days to complete the task if she worked alone.
Let Jane take 'y' days to complete the task if she worked alone.
Statement 1 of the question: They will complete the task in 20 days if they worked together.
In 1 day, Jose will complete 1/x of the task.
In 1 day, Jane will complete 1/y of the task.
Together, in 1 day they will complete 1/20 of the task.
Therefore,
In 1 day, Jane will complete 1/y of the task.
Together, in 1 day they will complete 1/20 of the task.
Therefore,
Statement 2 of the question: If Jose worked alone and completed half the work and then Jane takes over and completes the second half, the task will be completed in 45 days.
Jose will complete half the task in x/2 days.
Jane will complete half the task in y/2 days.
Or, x + y = 90 or x = 90 - y .... (2)
Jane will complete half the task in y/2 days.
Or, x + y = 90 or x = 90 - y .... (2)
Step 2: Solve the Two Equations and Compute x and y
Substitute the value of x as (90 - y) in the first equation.
Cross multiply and simplify: 1800 = 90y - y2
Or y2 - 90 + 1800 = 0.
Cross multiply and simplify: 1800 = 90y - y2
Or y2 - 90 + 1800 = 0.
The quadratic equation factorizes as (y - 60)(y - 30) = 0
So, y = 60 or y = 30.
If y = 60, then x = 90 - y = 90 - 60 = 30 and
If y = 30, then x = 90 - y = 90 - 30 = 60.
So, y = 60 or y = 30.
If y = 60, then x = 90 - y = 90 - 60 = 30 and
If y = 30, then x = 90 - y = 90 - 30 = 60.
The question states that Jane is more efficient than Jose. Therefore, Jane will take lesser time than Jose.
Hence, Jose will take 60 days to complete the task if he worked alone and Jane will take 30 days to complete the same task.
Choice C is the correct answer.
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Community Answer
Working together, Jose and Jane can complete an assigned task in 20 da...
Given information:
- Jose and Jane can complete a task together in 20 days
- Jose completes half the work alone in x days
- Jane completes the second half of the work alone in y days
- When Jose and Jane work separately, the task is completed in 45 days
Calculating individual work rates:
Let's assume the total work is represented by 1 unit.
- Together, Jose and Jane's work rate = 1/20
- Jose's work rate = 1/x (completing half the work)
- Jane's work rate = 1/y (completing the second half)
Formulating equations:
- When working together: 1/20 = 1/x + 1/y
- When working separately: Jose's work (1/2) + Jane's work (1/2) = 45 days
Solving the equations:
Given that Jane is more efficient than Jose, we can assume that Jane's work rate is faster. Since Jane completes the second half of the work, she should take less time than Jose to complete the same amount of work.
- From the equation 1/20 = 1/x + 1/y, we know that 1/x + 1/y is less than 1/20 (as Jane is more efficient)
- Therefore, when Jose completes half the work alone, it takes him longer than 20 days
- Hence, Jose will take 60 days to complete the task alone (option c)
Therefore, Jose will take 60 days to complete the task if he worked alone.
- Jose and Jane can complete a task together in 20 days
- Jose completes half the work alone in x days
- Jane completes the second half of the work alone in y days
- When Jose and Jane work separately, the task is completed in 45 days
Calculating individual work rates:
Let's assume the total work is represented by 1 unit.
- Together, Jose and Jane's work rate = 1/20
- Jose's work rate = 1/x (completing half the work)
- Jane's work rate = 1/y (completing the second half)
Formulating equations:
- When working together: 1/20 = 1/x + 1/y
- When working separately: Jose's work (1/2) + Jane's work (1/2) = 45 days
Solving the equations:
Given that Jane is more efficient than Jose, we can assume that Jane's work rate is faster. Since Jane completes the second half of the work, she should take less time than Jose to complete the same amount of work.
- From the equation 1/20 = 1/x + 1/y, we know that 1/x + 1/y is less than 1/20 (as Jane is more efficient)
- Therefore, when Jose completes half the work alone, it takes him longer than 20 days
- Hence, Jose will take 60 days to complete the task alone (option c)
Therefore, Jose will take 60 days to complete the task if he worked alone.
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Working together, Jose and Jane can complete an assigned task in 20 days. However, if Jose worked alone and completed half the work and then Jane takes over and completes the second half, the task will be completed in 45 days. How long will Jose take to complete the task if he worked alone? Assume that Jane is more efficient than Jose.a)25 daysb)30 daysc)60 daysd)65 dayse)36 daysCorrect answer is option 'C'. Can you explain this answer?
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Working together, Jose and Jane can complete an assigned task in 20 days. However, if Jose worked alone and completed half the work and then Jane takes over and completes the second half, the task will be completed in 45 days. How long will Jose take to complete the task if he worked alone? Assume that Jane is more efficient than Jose.a)25 daysb)30 daysc)60 daysd)65 dayse)36 daysCorrect answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Working together, Jose and Jane can complete an assigned task in 20 days. However, if Jose worked alone and completed half the work and then Jane takes over and completes the second half, the task will be completed in 45 days. How long will Jose take to complete the task if he worked alone? Assume that Jane is more efficient than Jose.a)25 daysb)30 daysc)60 daysd)65 dayse)36 daysCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Working together, Jose and Jane can complete an assigned task in 20 days. However, if Jose worked alone and completed half the work and then Jane takes over and completes the second half, the task will be completed in 45 days. How long will Jose take to complete the task if he worked alone? Assume that Jane is more efficient than Jose.a)25 daysb)30 daysc)60 daysd)65 dayse)36 daysCorrect answer is option 'C'. Can you explain this answer?.
Working together, Jose and Jane can complete an assigned task in 20 days. However, if Jose worked alone and completed half the work and then Jane takes over and completes the second half, the task will be completed in 45 days. How long will Jose take to complete the task if he worked alone? Assume that Jane is more efficient than Jose.a)25 daysb)30 daysc)60 daysd)65 dayse)36 daysCorrect answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Working together, Jose and Jane can complete an assigned task in 20 days. However, if Jose worked alone and completed half the work and then Jane takes over and completes the second half, the task will be completed in 45 days. How long will Jose take to complete the task if he worked alone? Assume that Jane is more efficient than Jose.a)25 daysb)30 daysc)60 daysd)65 dayse)36 daysCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Working together, Jose and Jane can complete an assigned task in 20 days. However, if Jose worked alone and completed half the work and then Jane takes over and completes the second half, the task will be completed in 45 days. How long will Jose take to complete the task if he worked alone? Assume that Jane is more efficient than Jose.a)25 daysb)30 daysc)60 daysd)65 dayse)36 daysCorrect answer is option 'C'. Can you explain this answer?.
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