Is This the Best Formula for Calculating Work and Time?

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SUMMARY

The formula for calculating work and time in a mathematical context is expressed as N1 * D1 * R = N2 * D2 * R, where N represents the number of persons, D denotes the number of days, and R is the rate of work done per person. This formula simplifies to N1 * D1 = N2 * D2 when the rate of work (R) is constant and cancels out. An example provided illustrates that if 20 men work for 10 days, the time taken by 30 men to complete the same work can be calculated without needing the specific rate of work. The derived solution indicates that it would take 20/3 days for 30 men to complete the task.

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  • Understanding of basic algebraic manipulation
  • Familiarity with the concept of work in mathematical terms
  • Knowledge of the relationship between manpower, time, and work
  • Ability to interpret word problems involving work and time
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momentum
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Hi,

whats the formula for work and Time ?


is it this ?

N1 * D1 * W1 =N2*D2*W2

where ,
N1=No of Persons
D1=No of days
W1=work


N2=No of Persons
D2=No of days
W2=work


is that's formula correct for work and time ?
 
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The simplest formula for mechanical work (in Physics) is
W = F s
Here, the force is contant and parallel to displacement and the body moves in a steady direction. W is work, F is force and s is displacement. The result is in Joules.

Unless you want manhours? What exactly are you trying to do? :)
 
no...there is no physics involved in it.

i'm talking about maths.

problems like..."20 man works for 10 days did a work, how long it would be taken by 30 man"?

this kind of problem

whats the formula ?

I have forgotten the formula...is it like same as i posted ?
 
N_1 R D_1 = W = N_2 R D_2

Where: N = number of men; R = rate of work done per man (assumed constant); D = days (or time); W = total work done.
 
>R = rate of work done per man (assumed constant);

what does it mean ?

can you give an example of it ?

thank you
 
Don't treat this as some esoteric formula from the ancients. It should be just "common sense", a variation of "Distance = Rate X time".

An example of R would be: a man can lift 50 bales of hay per day, so R = 50 bales/day/man.

So, if one man can lift 50 per day, how much total can be lifted in 3 days by 5 men?

Using W = N R D gives, W(total) = (5 men) (50 bales/day/man) (3 days) = 750 bales

But to solve a problem like " if 20 men working 10 days did a certain amount of work, how long would it take 30 men to do the same work?" you don't have to know R. Just use:

N_1 R D_1 = W = N_2 R D_2
(20)(R)(10) = (30)(R)(D_2)

Note that the Rs just drop out, and D_2 = 20/3 days.
 
Those are the dumbest of word problems. I would be tempted to answer : "The job would never get done, because the extra men would entice the entire lot to unionise and strike for better pay and conditions".
 
this is correct
N1 * D1 * W2 =N2*D2*W1
where ,
N1=No of Persons
D1=No of days
W1=work


N2=No of Persons
D2=No of days
W2=work
 
Except that just "work" is meaningless. I prefer Doc Al's "rate of work per day per man".
 
  • #10
yes bro u r right for "work" explanation but except tht mine formula is best one
 

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