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PS - Work rate question

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PS - Work rate question

by pratyoosh » Mon Nov 22, 2010 6:46 am
Hello,

Can someone please explain how to resolve the problem?

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

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by Geva@EconomistGMAT » Mon Nov 22, 2010 7:16 am
a good tip for rate questions where the work isn't defined (a room) is to plug in a number for the rate - preferably a number that is divisible by the other numbers mentioned in the question. the benefit here is the reduced tension of working with real numbers instead of fractions - it also helps you see things much clearer. for added effect, use real units - not "a wall", but "36 meters".

Let's say that the room is 36 meters (choose 36 because it is divisible by 6, 2 and 3).

Tom can do 36 meters in 6 hours, so tom's rate is 6 meters/hour
Peter can do 36 meters in 3 hours, or 12 meters/hour
John can do 36 meters in 2 hours , or 18 meter/hour.

Let's see how much work is actually done at each stage:
Tom works for 1 hour - does 6 meters, so 30 meters are left
Peter joins, and they work for an hour at their combined rate of 6+12=18 meters/hour. 18 more meters are done (total of 24 meters so far), 12 meters remaining.

John joins them - all three of them work at a rate of 6+12+18=36 metes/hour. The only have 12 meters left, so the polish that off in 12/36=1/3 of an hour.

what did the question ask? what fraction was done by Peter?
Peter worked for an hour (when he joined Tom), and another 1/3 of an hour when they were joined by John. Total of 1 hour and a third at his rate of 12 meters/hour, or 4/3*12 = 16 meters. so peter's fraction of the work is 16 out of the total of 36, or 16/36 = 4/9.
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by pratyoosh » Mon Nov 22, 2010 7:21 am
Hello Geva,

Thank you for the wonderful explanation, understood the problem in one shot !

Regards,
Pratyoosh.
Geva@MasterGMAT wrote:a good tip for rate questions where the work isn't defined (a room) is to plug in a number for the rate - preferably a number that is divisible by the other numbers mentioned in the question. the benefit here is the reduced tension of working with real numbers instead of fractions - it also helps you see things much clearer. for added effect, use real units - not "a wall", but "36 meters".

Let's say that the room is 36 meters (choose 36 because it is divisible by 6, 2 and 3).

Tom can do 36 meters in 6 hours, so tom's rate is 6 meters/hour
Peter can do 36 meters in 3 hours, or 12 meters/hour
John can do 36 meters in 2 hours , or 18 meter/hour.

Let's see how much work is actually done at each stage:
Tom works for 1 hour - does 6 meters, so 30 meters are left
Peter joins, and they work for an hour at their combined rate of 6+12=18 meters/hour. 18 more meters are done (total of 24 meters so far), 12 meters remaining.

John joins them - all three of them work at a rate of 6+12+18=36 metes/hour. The only have 12 meters left, so the polish that off in 12/36=1/3 of an hour.

what did the question ask? what fraction was done by Peter?
Peter worked for an hour (when he joined Tom), and another 1/3 of an hour when they were joined by John. Total of 1 hour and a third at his rate of 12 meters/hour, or 4/3*12 = 16 meters. so peter's fraction of the work is 16 out of the total of 36, or 16/36 = 4/9.
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by Bakhtior » Mon Nov 22, 2010 7:23 am
pratyoosh wrote:Hello,

Can someone please explain how to resolve the problem?

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

a whole job=1, Tom can do 1/6 part of whole job, then for an hour he has done 1/6 task, and remained 5/6 part of the whole. Peter can paint 1/3 part of whole task. Tom and Peter worked together for an hour, then (5/6)-(1/6)-(1/3)=(1/3). In the end all three have worked together (1/3)/(1/6+1/2+1/3)=1/3 They all worked 20 minutes or 1/3 hour, for 1/3 hour peter painted 1/9 part of whole task, 1/3+1/9=4/9
Answer E
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