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David completes 60% of an assigned task in 8 days and

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David completes 60% of an assigned task in 8 days and [#permalink] New post 06 Mar 2005, 15:39
David completes 60% of an assigned task in 8 days and realizes that he will be behind schedule at the present rate. He takes the assistance of his younger brother Ron who is one-third as efficient as David is and completes the assigned task on schedule. How many days did David and Ron work together?

a. 4
b. 6
c. 8
d. 12
e. 14
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 [#permalink] New post 06 Mar 2005, 16:10
i got 4 days.
total days req= 8/0.6
remaining days, d= (8/0.6)-8=16/3
days david and ron worked togather = (16/3)/4/3=4 days/
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 [#permalink] New post 06 Mar 2005, 17:42
Quote:
i got 4 days.
total days req= 8/0.6
remaining days, d= (8/0.6)-8=16/3
days david and ron worked togather = (16/3)/4/3=4 days/



Please explain how you got the last part "days david and ron worked together"

thanks.
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 [#permalink] New post 06 Mar 2005, 18:21
jma123,

16/3 is the remaining work

3/3 is the working rate of David
we know that Ron is 1/3d as efficient as David : 1/3
so they work at a rate of 4/3 days

(16/3) / (4/3)
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 [#permalink] New post 06 Mar 2005, 18:23
jma123 wrote:
Please explain how you got the last part "days david and ron worked together"thanks.


total days req= 8/0.6=40/3
remaining days, d= (8/0.6)-8=16/3
days david and ron worked togather = (16/3)/4/3=4 days

if he works alone, david takes 16/3 days to work at his current speed.
if he works togather with ron, whose speed is 1/3 of david's, it takes (16/3)/(4/3) days to finish the job. their combined speed =1+1/3=4/3. explain more, if any.
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 [#permalink] New post 06 Mar 2005, 19:23
4 days

In 8 days David finishes 60% of the job. So to complete the job he takes 40/3 days. So each day he finishes 3/40th of the job.

Ron is 1/3rd as efficient So he finishes 3/40*1/3 =1/40th of the job each day.

When both work together they finish 3/40+1/40= 4/40 each day

David had already finished 60% of the job . for the bal 40% he and Ron work together. So no of days both work together= 40/100* 40/4=4 days
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 [#permalink] New post 07 Mar 2005, 13:06
in 1 day david completes 1/(80/6) and in 8 days 8/(80/6)

ron is 1/3 as efficient and in 1 day he does 1/40

a complete job is equal to the sum of the fractional parts or is equal to one => 8/(80/6) + x/(80/6) + x/(40)=1 => solve for x

a little bit too long but i just want to show the formulas:

1/x + 1/x = 1/x => where x is the total time in hours and 1/x is the fractional part of job done in 1 hour

or

x/5 + x/8 = 1 => where x is the fractional part each does in x days; 5 and 8 are their rates
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 [#permalink] New post 15 Mar 2005, 10:01
it works quite easily if you take the total job as 100

say that in 8 days 60 has been done which equals 7.5 per day.

add in the bro at 1/3 of 7.5= 2.5 so now we are doing 10 per day look at the remaining 40 to be done and it is clearly 4 days.
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 [#permalink] New post 15 Mar 2005, 11:54
In 8 days 60/100 i.e. 3/5 work has been done.

If efficiency of David=1
efficiency of Ron=1/3

acording to formulae:

[man(d)*efficiency(d)*days worked(d)]/part of work done=(man(ron+david)*daysworked)/part of work done

(1*1*8)/(3/5)=(4x/3)/(2/5)
=>x=4 days
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 [#permalink] New post 15 Mar 2005, 12:06
christoph wrote:
in 1 day david completes 1/(80/6) and in 8 days 8/(80/6)

where does the 80 come from?

i did it a little differently
if 60% is done in 8 days 7.5% is done in 1 day
Ron is 1/3 as efficient so in 1 day he does 2.5% of the task
WHAT IS LEFT:
40%=7.5X+2.5X
X is time they both finish 40% in
4 days
(note: you can do this since all the numbers are in %, i guess it is the same as taking total of the job as 100
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 [#permalink] New post 15 Mar 2005, 12:13
a. 4

60% in 8 days
=> 100% in 40/3 days
& 40% in 16/3 days

1/3 efficient => 100% in 40 days => 40% in 16 days

together 1/t = 1/16 + 3/16
=> t = 4
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 [#permalink] New post 25 Mar 2005, 20:46
4 days seems right to me
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 [#permalink] New post 27 Mar 2005, 22:03
[quote="Caspace"]it works quite easily if you take the total job as 100

say that in 8 days 60 has been done which equals 7.5 per day.

add in the bro at 1/3 of 7.5= 2.5 so now we are doing 10 per day look at the remaining 40 to be done and it is clearly 4 days.[/quote]

This is essentially how I did it as well:

David completed 60% of the assignment in 8 days, which means that he completed 7.5% each day. His brother, Ron, completed 1/3 of that (or 2.5% each day). Together, they can complete 10% of the assignment each day. With 40% to complete, they worked together for 4 days to complete it.
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 [#permalink] New post 28 Mar 2005, 08:26
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If you want easy arithmatic here's how:

8 days D can finish 60%, therefore every four days he finishes 30%. His brother's speed is 1/3 of his. So every four days he finishes 10%. When they work together every four days they finish 30+10=40%, which is exactly what they needed.
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 [#permalink] New post 28 Mar 2005, 10:08
Rupstar wrote:
christoph wrote:
in 1 day david completes 1/(80/6) and in 8 days 8/(80/6)

where does the 80 come from?

i did it a little differently
if 60% is done in 8 days 7.5% is done in 1 day
Ron is 1/3 as efficient so in 1 day he does 2.5% of the task
WHAT IS LEFT:
40%=7.5X+2.5X
X is time they both finish 40% in
4 days
(note: you can do this since all the numbers are in %, i guess it is the same as taking total of the job as 100


i calculated his rate. in 8 days he does 60% and in 80/6 he does 100%.
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 [#permalink] New post 28 Mar 2005, 12:42
HongHu wrote:
If you want easy arithmatic here's how:

8 days D can finish 60%, therefore every four days he finishes 30%. His brother's speed is 1/3 of his. So every four days he finishes 10%. When they work together every four days they finish 30+10=40%, which is exactly what they needed.


I like ur ways to handle word problems, seems to be much faster if one can get a hang of it e.g. how did u know to think abt the amt of work in four days interval only, is it becose 40% work is left, is there any rule of thumb in this ?
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 [#permalink] New post 28 Mar 2005, 19:23
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Normally I'd do it to the smallest integer, and take it from there. This may not work every time though, but it's still good to save you a bit time if it works, and if it doesn't you simply have to go one step further.

For example in one of the other posts, we have
4m=6s or something like that
I'd simplify it to
2m=3s
instead of m=1.5s
Then when I want to know 16m it's easier to multiple 3 with 8, compare to 1.5 with 16.

Same thing with this one. We have 8 vs 60. It's easier to simplify it to 4 vs 30 than to simplify it to 1 vs 7.5. The 30 is also easier to handle when we want to multiply it by 1/3. Lots of GMAT math problems have nice numbers like this that would save you time if you know the trick.
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 [#permalink] New post 28 Mar 2005, 19:32
60% done in 8 days

Another person B joins A and is 1/3 efficient of A....

So man power is 4/3 times A .So work can be done in 3/4 time

So 60% can be done in (3/4)*8 = 6 days

So remaining 40% can be done in 4 days !!!
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Re: work/rate [#permalink] New post 29 Mar 2005, 12:11
cloaked_vessel wrote:
David completes 60% of an assigned task in 8 days and realizes that he will be behind schedule at the present rate. He takes the assistance of his younger brother Ron who is one-third as efficient as David is and completes the assigned task on schedule. How many days did David and Ron work together?

a. 4
b. 6
c. 8
d. 12
e. 14


Sometimes it helps to look at the answer list for clues... in this case, you're given that he's completed 60% in 8 days, so at the current rate he'd be complete in ~14 days. Cancel out c/d/e right away, as it won't take him longer with additional help. 6 days would be close without his brother, but it has to be less leaving you 4
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Re: work/rate   [#permalink] 29 Mar 2005, 12:11
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