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David completes 60% of an assigned task in 8 days and [#permalink]
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?

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.

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.

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.

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

[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.

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%.

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 ?

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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