SOLUTION: If 4 workers can paint a room in 3 hours, then approximately how long does it take 6 workers to paint the same room? Assume the time needed to paint the room is inversely proportio

Algebra ->  Graphs -> SOLUTION: If 4 workers can paint a room in 3 hours, then approximately how long does it take 6 workers to paint the same room? Assume the time needed to paint the room is inversely proportio      Log On


   

Question 1134353: If 4 workers can paint a room in 3 hours, then approximately how long does it take 6 workers to paint the same room? Assume the time needed to paint the room is inversely proportional to the number of workers.

Found 3 solutions by josgarithmetic, Edwin McCravy, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Rate of ONE worker, r;
unknown time for 6 workers, x;

system%284r%2A3=1%2C6r%2Ax=1%29

4r%2A3=6r%2Ax

4%2A3=6%2Ax

highlight%28x=2%29

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Assume the time needed to paint the room is inversely proportional to the
number of workers.

If 4 workers can paint a room in 3 hours,
matrix%281%2C5%2C%0D%0A4%2C%22%22%2C%22%22=%22%22%2C%22%22%2Ck%2F3%29%29
Put a 1 under the 4 so you can cross-multiply:

matrix%281%2C5%2C%0D%0A4%2F1%2C%22%22%2C%22%22=%22%22%2C%22%22%2Ck%2F3%29%29

matrix%281%2C5%2C%0D%0A1%2Ak%2C%22%22%2C%22%22=%22%22%2C%22%22%2C4%2A3%29%29

matrix%281%2C5%2C%0D%0Ak%2C%22%22%2C%22%22=%22%22%2C%22%22%2C12%29%29

Substitute 12 for k in

then approximately how long does it take 6 workers to paint the same room? 


Edwin

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The time needed to paint the room is inversely proportional to the number of workers. That means if the number of workers goes up by a factor of x the number of hours required goes down by that same factor.

In this problem, the number of workers goes up from 4 to 6; that's a factor of 6/4, or 3/2. The number of hours needed goes down by that same factor:

3%2F%283%2F2%29+=+3%2A%282%2F3%29+=+2

Less formally, you can just say that since the number of workers changes by a factor of 3/2 the number of hours changes by a factor of 2/3. 2/3 of 3 hours is 2 hours.