MGMAT RATIO Problem

[Khalid]

The following appears in the MGMAT practice problem under Word Transalation. Can someone please help me understand what I am doing wrong..thanks

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?


1/9
1/6
1/3
7/18
4/9


I started by assuming that there are 36 units of work

So in the first hour, Tom works alone at the rate of (1/6) job/hr
Tom finishes 6 uints of work alone ( 1/6*36 )

He is then Joined by Peter and their combined rate is ( 1/2 job per hr)
We started with 36, Tom has already finished 6 units, so we are left with 30 units
Thus, Peter and Tom together finish another 15 units of work ( 1/2 * 30 )
Of this 15 units, Tom finishes 5 unite and Peter finishes 10 units

Now they are joined by John, and their combined rate is 1j/hr
We are now left with 15 units of work out of the 36 that we started with ( 36 -15-6)
So of this 15 Peter completes 5 units of work ( 1/3 *15)
Tom finishes ( 1/6 * 15)
John finishes ( 1/2 *15)

Peter hence worked : (10+5 )= 15
Total unit = 36

So As a fraction Peter works (15/36=5/12)

But this is not even an answer choice..What am I doing wrong.....Thanks

[shaji]

Peter works for the entire period of time i.e. 7/3 hours(2hrs+1/3*1)

The work done by him is therefore 7/3*/6=7/18 which is the correct answer.

The following appears in the MGMAT practice problem under Word Transalation. Can someone please help me understand what I am doing wrong..thanks

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?


1/9
1/6
1/3
7/18
4/9


I started by assuming that there are 36 units of work

So in the first hour, Tom works alone at the rate of (1/6) job/hr
Tom finishes 6 uints of work alone ( 1/6*36 )

He is then Joined by Peter and their combined rate is ( 1/2 job per hr)
We started with 36, Tom has already finished 6 units, so we are left with 30 units
Thus, Peter and Tom together finish another 15 units of work ( 1/2 * 30 )
Of this 15 units, Tom finishes 5 unite and Peter finishes 10 units

Now they are joined by John, and their combined rate is 1j/hr
We are now left with 15 units of work out of the 36 that we started with ( 36 -15-6)
So of this 15 Peter completes 5 units of work ( 1/3 *15)
Tom finishes ( 1/6 * 15)
John finishes ( 1/2 *15)

Peter hence worked : (10+5 )= 15
Total unit = 36

So As a fraction Peter works (15/36=5/12)

But this is not even an answer choice..What am I doing wrong.....Thanks

[Kishore]

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?


1/9
1/6
1/3
7/18
4/9

Assume that Tom, Peter and John have worked for x hours to finish the remaining work.
This implies that Tom worked for 2+x hours, Peter worked for 1+x hours and John worked for x hours to complete the work.

So 1/6 * (2+x) + 1/3 * (1+x) + 1/2 * x = 1 (the sum of fractions of work completed by the 3 is equal to the entire work)

Solving for x, x = 1/3

Hence the fraction of work x
Tom completed is 1/6 * (2 + 1/3) = 1/6 * 7/3 = 7/18
Peter completed is 1/3 * (1 + 1/3) = 1/3 * 4/3 = 4/9
John completed is 1/2 * 1/3 = 1/6

Hence the answer is 4/9. The question should have been asking about Tom in which case the answer is 7/18 or the answer is 4/9

[shaji]

U R correct. A mishap with Tom.

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?


1/9
1/6
1/3
7/18
4/9

Assume that Tom, Peter and John have worked for x hours to finish the remaining work.
This implies that Tom worked for 2+x hours, Peter worked for 1+x hours and John worked for x hours to complete the work.

So 1/6 * (2+x) + 1/3 * (1+x) + 1/2 * x = 1 (the sum of fractions of work completed by the 3 is equal to the entire work)

Solving for x, x = 1/3

Hence the fraction of work x
Tom completed is 1/6 * (2 + 1/3) = 1/6 * 7/3 = 7/18
Peter completed is 1/3 * (1 + 1/3) = 1/3 * 4/3 = 4/9
John completed is 1/2 * 1/3 = 1/6

Hence the answer is 4/9. The question should have been asking about Tom in which case the answer is 7/18 or the answer is 4/9

[tyler.y.smith]

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?

If the question is asking about the fraction of the WHOLE job done by Peter

Why isn't the 2nd hour - where Peter and Tom complete 1/2 of the job working together - isn't (1/3)(1/2) = 1/6
Peter's contribution to the total job during this period is only 1/6th of the job

Then adding it to the 3rd hour - (1/3)(2/6) = 1/9

Peter's contribution to the whole job is actually

1/6 + 1/9 = 3/18+2/18 = 5/18

I know its not an option. But this makes much more sense than assuming Peter contributed in the 2nd hour 1/3 of the effort - which on his own would be true, but because he worked w/ Tom, contributed a bit less because of the shared work.

Please explain.

[jnelson0612]

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?

If the question is asking about the fraction of the WHOLE job done by Peter

Why isn't the 2nd hour - where Peter and Tom complete 1/2 of the job working together - isn't (1/3)(1/2) = 1/6
Peter's contribution to the total job during this period is only 1/6th of the job

Then adding it to the 3rd hour - (1/3)(2/6) = 1/9

Peter's contribution to the whole job is actually

1/6 + 1/9 = 3/18+2/18 = 5/18

I know its not an option. But this makes much more sense than assuming Peter contributed in the 2nd hour 1/3 of the effort - which on his own would be true, but because he worked w/ Tom, contributed a bit less because of the shared work.

Please explain.

Hi,
Let's think about this by first reviewing the rates and then walking through this slowly and carefully:
Tom can do the job in 6 hours, so he can do 1/6 of the job in one hour
Peter can do the job in 3 hours, so he can do 1/3 of the job in one hour
John can do the job in 2 hours, so he can do 1/2 of the job in one hour.

Tom starts and works by himself for one hour. In one hour, he knocks out 1/6 of the job. 5/6 of the job is left.

Now, here's where you got confused. For the second hour, Tom is joined by Peter. Tom can do 1/6 of the job in that hour and Peter can do 1/3 of the job in that hour. When two people are working together we add the rates. So together, they get 1/3 + 1/6 or 1/2 of the job done. Just because they are working together doesn't automatically make Peter less productive. Peter gets 1/3 of the *total* job done and when combined with Tom's work 1/2 of the total job is done in the second hour.

Okay, so hour one Tom got 1/6 of the job done and Tom and Peter got 1/2 of the job done in the second hour. We add those together and see that 1/3 of the job is remaining.

So now, we need to add the rates of all three: (1/6 + 1/3 + 1/2) which equals 1. All three together can do the job in one hour. Since we only have 1/3 of the job remaining, we only need the three to work 1/3 of an hour.

How much does Peter do in that last 1/3 hour? Rate * Time = Work, or 1/3 * 1/3=1/9.

How much work does Peter do overall? 1/3 of the job in the second hour + 1/9 of the job in the third hour, or 4/9 of the total job.

Does this make more sense?

[tyler.y.smith]

Jamie,

The lightbulb just clicked - thank you for explaining it so thoroughly.

Tyler,

[RonPurewal]

cool.

[actleader]

Having found that remaining part of wall to be done is 1/3,
and keeping in mind time need for each of "workers" to finish
we may presume the following ratio:
T:P:J as 1/6:1/3:1/2, and find out P's share as
(1/3)/(1/6+1/3+1/2) = 1/3;
so as part of wall to be done 1/3, and the part "allocated" to P:
1/3*1/3=1/9, then
1/3+1/9=4/9

[tim]

let us know if there are any further questions on this one..