SOLUTION: if it takes 6 days for 6 workers to build a garage, how long would it take 9 workers?

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Question 1150533: if it takes 6 days for 6 workers to build a garage, how long would it take 9 workers?
Found 3 solutions by Edwin McCravy, ikleyn, greenestamps:
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
if it takes 6 days for 6 workers to build a garage, how long would it take 9 workers?
We have 6 workers the first time and 9 workers the second time.

The least common multiple of 6 workers and 9 workers is 18 workers.

if it takes 6 days for 6 workers to build a garage, then what about 18 workers?
They would work 3 times as fast so it would take them only 1/3 as long as it
took 6 workers, or only 2 hours.

So if it takes 18 workers 2 hours to build a garage, then 9 workers would take
twice as long, so it would take them 4 hours.

Edwin


Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

The entire job is  6*6 = 36  worker-days  (man-days,  as it was called long time ago . . . ).


Therefore,  9 workers will complete this job in   36%2F9 = 4 days.         ANSWER


ANSWER.   9 workers will complete this job in  4  days.


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I remember,  we solved such problems when I was at my  4-th  or  5-th grade class.

All the students loved this type of problems,  because  EVERYBODY  knew how to solve them.

So,  ignore explanations from  Edwin  (with his Least Common Multiplies - they are  IRRELEVANT),


                and use the mantra from my post . . .


/\/\/\/\/\/\/\

After reading the post by @greenestamps.

    Yes, you can use the method these two gentlemen propose you.


    But it is the same, as to fly from Chicago  to Indianapolis with intermediate landing in Denver.


    The way I propose in my post is the standard direct straightforward shortest Algebra way for this type of problems.


Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


You would do well to ignore the proclamation by tutor @ikleyn about her mantra.

Find your own mantra.

The solution method shown by tutor @edwin is perfectly valid. You might find it is more to your liking than hers.

In my opinion, her use of man-days is "irrelevant"....

9 workers is 3/2 times as many as 6 workers; the amount of time required is going to be 2/3 as much. 2/3 of 6 days is 4 days.

Again, ignore anybody who tells you a particular method of solving a problem is wrong.

Keep your mind open and find a solution method that YOU like.