SOLUTION: Confusion with basic division and multiplication. If 8 men can chop 9 cords of wood in 6 hours, how amny hours will it take 4 men to chop 3 cords of wood? I saw an answer to

Question 983941: Confusion with basic division and multiplication.
If 8 men can chop 9 cords of wood in 6 hours, how amny hours will it take 4 men to chop 3 cords of wood?
I saw an answer to this that went something like
8M takes 6H to chop 9C
1M takes (6*8)=48H to chop 9C
1M takes (48/3)=16H to chop 3C
Hence, 4M takes (16/4)=4h to chop 3c
Answer 4 Hours
I don't understand any of this. Why is it 6*8? for one person to cut 9C?
then why does the hour change why is 48 then divided by 3? or maybe I copied that wrong?
and finally where does the 16 come from and why is it being divided by 4? It doesn't make sense to me.
Please explain
Thanks
Found 2 solutions by macston, josgarithmetic:
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
.
One man working one hour is 1 man-hour.
Two men working one hour is 2 man-hours.
.
If 8 men can chop 9 cords of wood in 6 hours, how many hours will it take 4 men to chop 3 cords of wood?
.
8 men working 6 hours is (8men) x (6 hrs)=48 man-hours
48 man hours/9 cords=5.33 man-hours/cord
It takes 5.33 man-hours to chop 1 cord of wood.
To chop 3 cords would take 3 cords x 5.33 man-hours/cord=16 man-hours.
It would take one man 16 hours to chop 3 cords.
For four men to provide 16 man-hours, they must work 4 hours
(16 man-hours/4 men)=4 hours.
So it would take 4 men 4 hours to chop 3 cords.
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
If you are comfortable with the basic algebra needed, then the example problem is best understood
rate of doing work.
People working on the same job together do the work according to the sum of their individual rates.
Rate of wood chopping multiplied by time of wood chopping becomes amount of wood chopped.
RT=W to relate rate, time, and amount of wood or amount of Work.

The example gives two descriptions.
Assign some variables, but being done with different names than your example steps are showing.
r, the rate for one wood-chopper in unit of CORD/HOUR
Time will be in HOUR unit
WORK will be in CORD unit ("cords of wood").

8 men, 9 cords, 6 hours:

4 men, 3 cords, how much time:
We need another variable, ...
Let t be the time in hours which we want to solve.

We formed two equations making a system of equations.

This can be solved for each of the two variables, r and t.
CAN YOU solve this system?
Solve the first equation for r.
Use what you find for r in the other equation and solve for t.

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