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Mathdummy67

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Reciprocals, mixed numbers, improper fractions and "manpower"problems

Hey guys.  I have an upcoming  plumbing exam that has questions on "manpower."   I am having trouble.  I sorta understand the way its done, but the LIGHTBULB is not really going off.  I'll post the 4 problems that we were given to work on. Thank you in advance. the Math Dummy

1) If plumber A does a job in six days, and plumber B does the same job in 3 days, how long will it take the two of them working together to do the job?

2) Plumbers A and B working together do a JOB in 4 1/2 days.   Plumber B working alone is able to do the job in 10 days.  How long would it take A, working alone, to do the job?

3) If Plumber A can do a job in 6 days, which plumber B can do in 5 1/2, and plumber C can do in  2 1/5ths days, how long would it take with ALL doing job together?

4)  It is estimated that it will take 6 plumbers 20 days to install a drainage system.  After 8 plumbers worked 5 days, 8 additional plumbers were sent to job.  the total installation time  is?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Reciprocals, mixed numbers, improper fractions and "manpower"problems

Hi;

I have not done one of these in a long time, hope I am getting it right.

1)

A = 1 / 6 per day

B = 1 / 3 per day

Can you solve for x?

2)

Again, you have to solve for A and B...

Now you try 3 and 4.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: Reciprocals, mixed numbers, improper fractions and "manpower"problems

There problems are often referred to as "work word problems". Some of what I will post is advice from http://gmatclub.com/forum/work-word-pro … 87357.html.

I highly recommend you checkout the following websites as well for more information and practice
http://gmatclub.com/forum/work-word-pro … 87357.html

http://www.purplemath.com/modules/workprob.htm

There is a somewhat general way of solving these problems. However, do not go about these problems trying to remember some formula. Once you understand the logic underlying the above steps, you will have all the information you need to solve any similar word problem.

STEP 1: Calculate how much work each person/machine does in one unit of time (could be days, hours, minutes, etc).

How do we do this? Simple. If we are given that A completes a certain amount of work in X hours, simply reciprocate the number of hours to get the per hour work. Thus in one hour, A would complete

of the work. But what is the logic behind this? Let me explain with the help of an example.

Assume we are given that Jack paints a wall in 5 hours. This means that in every hour, he completes a fraction of the work so that at the end of 5 hours, the fraction of work he has completed will become 1 (that means he has completed the task).

Thus, if in 5 hours the fraction of work completed is 1, then in 1 hour, the fraction of work completed will be (1*1)/5

STEP 2: Add up the amount of work done by each person/machine in that one unit of time.

This would give us the total amount of work completed by both of them in one hour. For example, if A completes

of the work in one hour and B completes

of the work in one hour, then TOGETHER, they can complete

of the work in one hour.

STEP 3: Calculate total amount of time taken for work to be completed when all persons/machines are working together.

The logic is similar to one we used in STEP 1, the only difference being that we use it in reverse order. Suppose

. This means that in one hour, A and B working together will complete

of the work. Therefore, working together, they will complete the work in Z hours.

Good luck on your exam!

Last edited by ShivamS (2014-05-31 11:58:38)