SOLUTION: 4 men can do a piece of work in 8 days how many days would it take 16 men at the same rate

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 4 men can do a piece of work in 8 days how many days would it take 16 men at the same rate       Log On


   

Question 1189730: 4 men can do a piece of work in 8 days how many days would it take
16 men at the same rate
Found 4 solutions by Edwin McCravy, ikleyn, josgarithmetic, greenestamps:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Instead of doing your homework for you, I'll do another one exactly
like it with different numbers.

3 men can do a piece of work in 9 days. How many days would it take
9 men at the same rate
The more the men the fewer the days, so days and men are inversely 
proportional.

Days=k%2FMen
9=k%2F3
27=k

Days=27%2FMen
Days=27%2F9
Days=3

Now do yours the same way.

Edwin

Answer by ikleyn(52806) About Me  (Show Source):
You can put this solution on YOUR website!
.

See my lesson

    - Rate of work problems

in this site.   Find there many similar and different problems solved with detailed explanations.


Consider this lesson as your textbook,  handbook,  guide,  tutorials and  (free of charge)  home teacher.


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Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
1, "a piece of work", the one job to be done
r, rate of work for any one man
x, the unknown number of days


system%284r%2A8=1%2C16rx=1%29

Could you think carefully about the description, and guess, 2 days?

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


Both of the responses you have received use some kind of formal algebra to solve the problem, as do all the examples in the lesson referenced by the third tutor.

Those methods are fine, and they might need to be use in more complicated problems. But this kind of basic problem can be solved in very little time informally, using logical reasoning.

In this example, we are told that 4 men can do a job in 8 days; then we are asked to find how many days it would take 16 men to do the job.

Common sense tells us that increasing the number of workers by a factor of 4 will decrease the required amount of time by a factor of 4.

ANSWER: 8/4 = 2 days