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Tom, working alone, can paint a room in 6 hours. Peter and John, working independently, can paint the same room in 3 hours and 2 hours, respectively. Tom starts painting the room and works on his own for one hour. He is then joined by Peter and they work together for an hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?
- a)1/9
- b)1/6
- c)1/3
- d)7/18
- e)4/9
Correct answer is option 'E'. Can you explain this answer?
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Verified Answer
Tom, working alone, can paint a room in 6 hours. Peter and John, worki...
Peter's individual rate is 1 job / 3 hours.
Peter joins Tom and they work together for another hour; Peter and Tom's respective individual rates can be added together to calculate their combined rate: 1/6 + 1/3 = 1/2.
Working together then they will complete 1/2 of the job in the 1 hour they work together.
Peter joins Tom and they work together for another hour; Peter and Tom's respective individual rates can be added together to calculate their combined rate: 1/6 + 1/3 = 1/2.
Working together then they will complete 1/2 of the job in the 1 hour they work together.
At this point, 2/3 of the job has been completed (1/6 by Peter alone + 1/2 by Peter and Tom), and 1/3 remains.
When John joins Tom and Peter, the new combined rate for all three is: 1/6 + 1/3 + 1/2 = 1.
The time that it will take them to finish the remaining 1/3 of the job can be solved:
rt = w → (1)(t) = 1/3 → t = 1/3.
The question asks us for the fraction of the job that Peter completed. In the hour that Peter worked with Tom he alone completed: rt = w → w = (1/3)(1) = 1/3 of the job.
In the last 1/3 of an hour that all three worked together, Peter alone completed:
(1/3)(1/3) = 1/9 of the job.
Adding these two values together, we get 1/3 + 1/9 of the job = 4/9 of the job.
The time that it will take them to finish the remaining 1/3 of the job can be solved:
rt = w → (1)(t) = 1/3 → t = 1/3.
The question asks us for the fraction of the job that Peter completed. In the hour that Peter worked with Tom he alone completed: rt = w → w = (1/3)(1) = 1/3 of the job.
In the last 1/3 of an hour that all three worked together, Peter alone completed:
(1/3)(1/3) = 1/9 of the job.
Adding these two values together, we get 1/3 + 1/9 of the job = 4/9 of the job.
The correct answer is E.
Most Upvoted Answer
Tom, working alone, can paint a room in 6 hours. Peter and John, worki...
To solve this problem, we need to calculate the fraction of the whole job that was done by Peter.
Let's first determine the rates at which each person can paint the room. Tom takes 6 hours to paint the room, so his rate is 1/6 of the room per hour. Peter takes 3 hours to paint the room, so his rate is 1/3 of the room per hour. John takes 2 hours to paint the room, so his rate is 1/2 of the room per hour.
Now, let's calculate the work done by each person in the first hour:
- Tom worked alone for one hour, so he completed 1/6 of the room.
- Peter and Tom worked together for one hour. Since they have a combined rate of 1/6 + 1/3 = 1/2 of the room per hour, they completed 1/2 of the room in that hour. However, Tom already completed 1/6 of the room, so Peter's contribution is 1/2 - 1/6 = 1/3 of the room.
- Finally, Tom, Peter, and John worked together for the remaining time. Their combined rate is 1/6 + 1/3 + 1/2 = 7/6 of the room per hour. Since they worked for 3 hours (total time - Tom's first hour - Tom and Peter's hour), they completed 3 * 7/6 = 7/2 of the room. However, Tom already completed 1/6 of the room, and Peter completed 1/3 of the room, so John's contribution is 7/2 - 1/6 - 1/3 = 7/6 - 1/6 - 2/6 = 4/6 = 2/3 of the room.
Therefore, the fraction of the whole job done by Peter is 1/3 + 2/3 = 3/3 = 1.
Let's first determine the rates at which each person can paint the room. Tom takes 6 hours to paint the room, so his rate is 1/6 of the room per hour. Peter takes 3 hours to paint the room, so his rate is 1/3 of the room per hour. John takes 2 hours to paint the room, so his rate is 1/2 of the room per hour.
Now, let's calculate the work done by each person in the first hour:
- Tom worked alone for one hour, so he completed 1/6 of the room.
- Peter and Tom worked together for one hour. Since they have a combined rate of 1/6 + 1/3 = 1/2 of the room per hour, they completed 1/2 of the room in that hour. However, Tom already completed 1/6 of the room, so Peter's contribution is 1/2 - 1/6 = 1/3 of the room.
- Finally, Tom, Peter, and John worked together for the remaining time. Their combined rate is 1/6 + 1/3 + 1/2 = 7/6 of the room per hour. Since they worked for 3 hours (total time - Tom's first hour - Tom and Peter's hour), they completed 3 * 7/6 = 7/2 of the room. However, Tom already completed 1/6 of the room, and Peter completed 1/3 of the room, so John's contribution is 7/2 - 1/6 - 1/3 = 7/6 - 1/6 - 2/6 = 4/6 = 2/3 of the room.
Therefore, the fraction of the whole job done by Peter is 1/3 + 2/3 = 3/3 = 1.
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Tom, working alone, can paint a room in 6 hours. Peter and John, working independently, can paint the same room in 3 hours and 2 hours, respectively. Tom starts painting the room and works on his own for one hour. He is then joined by Peter and they work together for an hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?a)1/9b)1/6c)1/3d)7/18e)4/9Correct answer is option 'E'. Can you explain this answer?
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Tom, working alone, can paint a room in 6 hours. Peter and John, working independently, can paint the same room in 3 hours and 2 hours, respectively. Tom starts painting the room and works on his own for one hour. He is then joined by Peter and they work together for an hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?a)1/9b)1/6c)1/3d)7/18e)4/9Correct answer is option 'E'. 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 Tom, working alone, can paint a room in 6 hours. Peter and John, working independently, can paint the same room in 3 hours and 2 hours, respectively. Tom starts painting the room and works on his own for one hour. He is then joined by Peter and they work together for an hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?a)1/9b)1/6c)1/3d)7/18e)4/9Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Tom, working alone, can paint a room in 6 hours. Peter and John, working independently, can paint the same room in 3 hours and 2 hours, respectively. Tom starts painting the room and works on his own for one hour. He is then joined by Peter and they work together for an hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?a)1/9b)1/6c)1/3d)7/18e)4/9Correct answer is option 'E'. Can you explain this answer?.
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