Understanding Time & Work formula

Question

Let
M=Men, D=Days, H=Hours, W=Work
M ∝ W (M is directly proportional to W)
D ∝ W
H ∝ W
MDH ∝ W
MDH = kW
MDH/W = k
I know MDH represents Total Men hour work and W represents 1 unit of work. Then what does the ratio MDH/W represents.

mikemcgarry · Answer

Dear 22990atinesh , I'm happy to respond. :-)

First of all, I'll suggest that if you put the k on the other side of the equation, it will be much more sensible: kMDH = W So that k = W/(MDH) which would make it vaguely rate-like. Work per man-hour-days, something like that. I will say, I don't think know this formula is going to help you on the GMAT. You do have to know the basic idea of work rate R, where A = RT (A is the amount of work done). The GMAT tends not to ask a lot of questions about the amount of work done when you change the number of men or number of machines, and I have absolutely never seen anything testing the details of hours per day vs. days worked. The GMAT is much more apt to ask about two (or more) different machines (or people) working at different rates; the GMAT loves questions of that form --- A works at this rate, B works at that rate, what happens when the work together? etc. See this blog for a further discussion: https://magoosh.com/gmat/2012/gmat-work-rate-problems/ This formula you have, and worrying about the meaning of k, is not going to help you at all on the work questions that are most typical on the GMAT. Does all this make sense? Mike :-)

22990atinesh · Answer

Hello mikemcgarry thanx for your response,
I'm not a GMAT Aspirant, I'm just clearing my basic doubts of some aptitude topics.

JapinderKaur · Answer

Dear 22990atinesh

It's good that you are curious to understand the real-world significance of mathematical formulas.

Coming to your ques,  k = \frac{MDH}{W} 
 =  \frac{Total man-hours worked}{Total units of work done} 
= Man-hours required per unit of work

You can appreciate that this ratio will be useful for some companies. For example, let's say, a car company is debating whether to purchase a few automation machines or not. They may use this ratio in their decision-making. For example, assembling of 1 car may normally take 100 man-hours (that is, k=100), but with the automation machines, it may take only 40 man-hours (that is, k'= 40). This looks like an attractive proposition! Of course, the management will also consider other factors, like costs, in making their decision.

rajatjain14 · Answer

Dear 22990atinesh,

This MDH = k(constant) * W can be used to solve problems where 2 situations in terms of men, days and hours are given:

\frac{M1 * D1 * H1}{M2 * D2 * H2} = \frac{W1}{W2}  ,

For example,  
If 6 men working 5 days for 8 hours each can finish a task. How many men would be needed for 4 days for 6 hours each to finish half the task?

Answer:

\frac{M1 * D1 * H1}{M2 * D2 * H2} = \frac{W1}{W2}

=  \frac{6 * 5 * 8}{M2 * 4 * 6} = \frac{1}{0.5}

Solving,

we get M2 = 5 men

Rgds,
Rajat

22990atinesh · Answer

Thanx MavenQ, I think I get it .You are trying to say that total Man hour/unit work is constant i.e. MDH/W=k. for example we have given that 2 Men working 3 hours/day works for 4 days to complete a work (unit of work). Calculate how many days required by 1 man working 2 hours/day to complete the 1/2 of that work.

Sol: As we know Man hour/unit work is constant. Hence  \frac{M_1D_1H_1}{W_1}=\frac{M_2D_2H_2}{W_2} 
Now we can easily plug data in LHS of the above equation. But for RHS as we know, we have to calculate days required by 1 man working 2 hours/day to complete the  1/2 of that work . so we have to double the total Man hour in RHS i.e.

\frac{2*4*3}{1}=\frac{2*(1*X*2)}{1}

\frac{2*4*3}{1}=\frac{(1*X*2)}{1/2}

X=6

Correct If I did something wrong.

June29 · Answer

Hi Mike,  mikemcgarry 
Could you explain how do we work this question :
Computer hackers can scan and infect 10 computers in 5 hours.If this group of hackers want to scan and infect 20 computers in 8 hours ,how many new computer hackers do they need to recruit and join their team in-order to accomplish this task,assuming all hackers work at the same rate.
How do we solve this GMAT question

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Understanding Time & Work formula

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