Question 1092198: A contract for laying 400m of drain pipe requires 24 men working for 20 days. What length of the pipe would be laid by 30 men in 18 days .
Found 3 solutions by josgarithmetic, greenestamps, ikleyn:
Answer by josgarithmetic(39617)   (Show Source):
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
I personally nearly always find it easiest to work problems like this by looking at how the number of feet of pipe is affected by the change in each of the other parameters in the problem.
30 men instead of 24: an increase by a factor of 30/24, or 5/4.
18 days instead of 20: a decrease by a factor of 18/20, or 9/10.
Applying these factors to the given number of 400 feet of pipe, the new number of feet of pipe is
Answer by ikleyn(52778)  (Show Source):
You can put this solution on YOUR website! .
For many similar solved problems of this type ("rate of work problems") see the lesson
- Rate of work problems
in this site. Consider that solved problems as your samples.
There are TWO major approaches to solve such problems.
One approach is based on counting "man-hours" or "man-days", when you write equation for man-hours or man-days.
It works smoothly in simple problems, but not always so smoothly in more complicated problems.
Another approach is writing equation that states that the productivity ("rate of work") is the same for
two different scenarios that are described in the condition.
Based on my expertise, this method works always, and you always can control your solution.
And I definitely and certainly do not advise you to use the approach described by the tutor @greenestamps,
because in complicated problems it inevitable will lead you to errors.
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Now, regarding your concrete problem,
rate of work in the first scenario is  meters of pipe per one worker per day.
In the second scenario, the pipe length "x" is unknown, but you easily and automatically can write an expression
for the rate of work as  .
Since the rate of work is the same (is assumed to be the same), it gives you an equation
= . (1)
Now you should express x =  as the unknown term of a proportion, using the rules of proportions,
and calculate the answer
x = 450 meters.
That's all.
Again, the equation (1) says that the rate of work is the same in two different scenarios.
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When students solve word problems in Algebra, their major concern is "how to write an equation".
In "rate of work problems" always think on "rate of work" first, and it always will lead you to success.
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