SOLUTION: 3 men can unload 270 kg of goods in 4 hours. How many men are needed to unload 540 kg of goods in 3 hours?

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Question 1200641: 3 men can unload 270 kg of goods in 4 hours. How many men are needed to unload 540 kg of goods in 3 hours?
Found 3 solutions by ikleyn, greenestamps, josgarithmetic:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
3 men can unload 270 kg of goods in 4 hours. How many men are needed
to unload 540 kg of goods in 3 hours?
~~~~~~~~~~~~~~~~~~ 

Let "m" be "how many men are needed", i.e. the quantity under the problem's question.


Write the proportion, which says that the rate of work for each man is the same in both cases

     = .


Simplify a bit

     = .


From it, find m

    m =  = 4*2 = 8.


ANSWER.  8 men are needed.

Solved.

----------------

To see many other similar  (and different)  problems,  solved by the same method,  look into the lesson
    - Rate of work problems
in this site.

It was written specially for you,  to make your horizon  WIDER  and your knowledge  DEEPER.


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


The response from the other tutor shows a typical formal way of solving a problem like this.

In my experience, many students find it difficult to set the problem up correctly using that method.

I find the following informal method much more to my liking. See if it "works" for you.

We start with 3 men, and we need to determine the number of men needed when the numbers change. Consider how the number of men changes when each of the other numbers changes.

The number of kg doubles, from 270kg to 540kg. More kg means more men; doubling the number of kg doubles the number of men required.

The number of hours decreases from 4 to 3; i.e., the number of hours gets multiplied by 3/4. Fewer hours means more men are required, so the number of men needs to get multiplied by 4/3.

The number of men started at 3; it got multiplied by 2 because of the increase in the number of kg; and it got multiplied by 4/3 because of the decrease in the number of hours:

(3)(2)(4/3) = 8

ANSWER: 8 hours
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
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3 men can unload 270 kg of goods in 4 hours.
-----------------------------------------------
r, rate for 1 man


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How many men are needed to unload 540 kg of goods in 3 hours?
--------------------------------------------------------------

r, rate for 1 man
n, number of men


system to solve, for n (since factor r will cancel)


Eq.2 divided by Eq.1
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