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Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?
- a)46/9
- b)50/9
- c)50/11
- d)36/7
- e)210/41
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Working alone at their respective constant rates, A can complete a tas...
Working alone at a constant rate if A takes 'a' days to complete a task, A will complete 1/a of the task in a day.
Step 1: Translate words into mathematical expressions
A will complete 1/a of the task in a day.
Therefore, in 2 days A will complete 2/a of the task in a day.
Similarly, A will complete 5/a of the task in 5 days.
Step 1: Translate words into mathematical expressions
A will complete 1/a of the task in a day.
Therefore, in 2 days A will complete 2/a of the task in a day.
Similarly, A will complete 5/a of the task in 5 days.
If A starts, they finish the task in exactly 10 days.
A starts and works for 2 days. So, A will work on day 1 and day 2.
Then B will work for the next 2 days. B will work on day 3 and day 4.
A will continue for the next 2 days. i.e., on day 5 and day 6.
B will work on day 7 and day 8.
A will for the last 2 days i.e., day 9 and day 10.
Therefore, A will work on day 1, day 2, day 5, day 6, day 9, and day 10. i.e., for 6 days.
And B will work on day 3, day 4, day 7, and day 8. i.e., for 4 days.
In 6 days A will complete 6/a of the task.
In 4 days B will complete 4/a of the task.
With A working 6 days and B working 4 days, the task is completed.
If B starts, they finish the task they take half a day more. i.e., 10.5 days.
Therefore, B will work on day 1, day 2, day 5, day 6, day 9, and day 10. i.e., for 6 days.
And A will work on day 3, day 4, day 7, day 8 and half a day on day 11. i.e., for 4.5 days.
In 6 days B will complete 6/b of the task.
In 4 days A will complete 4.5/a of the task.
With B working 6 days and A working 4.5 days, the task is completed.
Step 2: Solve the two equations
Solving the two equations we get a = 9 days and b = 12 days.
The question: How long does it take to complete the task if they both work together?
Working together A and B will complete
th of the task in a day.
Hence, they will complete the task in 36/7 days.
Choice D is the correct answer.
A starts and works for 2 days. So, A will work on day 1 and day 2.
Then B will work for the next 2 days. B will work on day 3 and day 4.
A will continue for the next 2 days. i.e., on day 5 and day 6.
B will work on day 7 and day 8.
A will for the last 2 days i.e., day 9 and day 10.
Therefore, A will work on day 1, day 2, day 5, day 6, day 9, and day 10. i.e., for 6 days.
And B will work on day 3, day 4, day 7, and day 8. i.e., for 4 days.
In 6 days A will complete 6/a of the task.
In 4 days B will complete 4/a of the task.
With A working 6 days and B working 4 days, the task is completed.
If B starts, they finish the task they take half a day more. i.e., 10.5 days.
Therefore, B will work on day 1, day 2, day 5, day 6, day 9, and day 10. i.e., for 6 days.
And A will work on day 3, day 4, day 7, day 8 and half a day on day 11. i.e., for 4.5 days.
In 6 days B will complete 6/b of the task.
In 4 days A will complete 4.5/a of the task.
With B working 6 days and A working 4.5 days, the task is completed.
Step 2: Solve the two equations
Solving the two equations we get a = 9 days and b = 12 days.
The question: How long does it take to complete the task if they both work together?
Working together A and B will complete
th of the task in a day.Hence, they will complete the task in 36/7 days.
Choice D is the correct answer.
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Community Answer
Working alone at their respective constant rates, A can complete a tas...
X hours and B can complete the same task in y hours. Let's assume that A completes 1/x of the task in 1 hour and B completes 1/y of the task in 1 hour.
If they work together, the amount of work they complete in 1 hour is the sum of their individual rates. So, A and B together complete 1/x + 1/y of the task in 1 hour.
To find the time it takes for them to complete the task together, we can calculate the reciprocal of their combined rate. The combined rate is 1/x + 1/y, so the time it takes for them to complete the task together is 1/(1/x + 1/y).
Simplifying this expression, we can find a common denominator for 1/x and 1/y, which is xy. Multiplying 1/x by y/y and 1/y by x/x, we get y/xy and x/xy, respectively. Adding these fractions, we have (y + x)/(xy).
Therefore, the time it takes for A and B to complete the task together is 1/(1/x + 1/y) = xy/(x + y).
If they work together, the amount of work they complete in 1 hour is the sum of their individual rates. So, A and B together complete 1/x + 1/y of the task in 1 hour.
To find the time it takes for them to complete the task together, we can calculate the reciprocal of their combined rate. The combined rate is 1/x + 1/y, so the time it takes for them to complete the task together is 1/(1/x + 1/y).
Simplifying this expression, we can find a common denominator for 1/x and 1/y, which is xy. Multiplying 1/x by y/y and 1/y by x/x, we get y/xy and x/xy, respectively. Adding these fractions, we have (y + x)/(xy).
Therefore, the time it takes for A and B to complete the task together is 1/(1/x + 1/y) = xy/(x + y).
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Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?a)46/9b)50/9c)50/11d)36/7e)210/41Correct answer is option 'D'. Can you explain this answer?
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Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?a)46/9b)50/9c)50/11d)36/7e)210/41Correct answer is option 'D'. 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 alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?a)46/9b)50/9c)50/11d)36/7e)210/41Correct answer is option 'D'. 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 alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?a)46/9b)50/9c)50/11d)36/7e)210/41Correct answer is option 'D'. Can you explain this answer?.
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