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David completes 60% of an assigned task in 8 days and [#permalink]
 06 Mar 2005, 16:39
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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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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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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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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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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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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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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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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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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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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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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4 days seems right to me
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[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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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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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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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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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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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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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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