Quake3World

mjrpes wrote:I think we both solved it from different angles. I don't know how you got x = -9.5 Jules

mjrpes wrote:Let's start with the following equations that express the overall work done per worker:

x * e = A
x * e = B

Where x is the number of hours worked, e is the efficiency of the worker, and A and B stand for the overall amount of work done over time (hours * efficiency = total work done)

We can define efficiency e as a coefficient that stands for how many 'tasks per hour' a worker can complete.

STEP 1: The general equation

• Let's start with the general equation. We want to find the time needed for two people to complete one task. The equation can be worded as:
  
  "The total work output of both workers combined to complete one task"
  
  Which looks like:
  
  <Work Done by A> + <Work Done by B> = 1 Task
  
  We will define the work done as:
  
  <Work Done by Person A> = d1
  <Work Done by Person B> = d2
  
  So that:
  
  d1 + d2 = 1

STEP 2: Equation for work done per worker:

• Now we need to find equation for the work done portion of the general equation above. This can be written out as:
  
  time (hours) * efficiency (tasks/hour) = Work Done (tasks)
  
  Notice the units we are using:
  
  hours * tasks/hour = task
  
  This makes sense because the hours cancel out!!
  
  Let's set our variables. So, per worker, we will use variables
  
  <hours worked> = t1, t2
  <efficiency> = e1, e2
  
  Where Worker A uses t1, e1 and Worker B uses t2, e2
  
  Using these variables for each worker we get the equations:
  
  t1 * e1 = d1
  t2 * e2 = d2
  
  Substituting into the equation above, our new equation looks like
  
  (t1 * e1) + (t2 * e2) = 1

STEP 3: Get efficiency:

• We know that for worker A, it takes him 5 hours to do one task. And for worker B it takes 15 hours to do one task. So their rate is
  
  5 hours per task = 1/5 tasks per hour
  15 hours per task = 1/15 tasks per hour
  
  So we know that:
  
  e1 = 1/5
  e2 = 1/15
  
  Substituting this into our equation, we get
  
  t1 * (1/5) + t2 * (1/15) = 1

STEP 4: Deal with the amount of time worked for both

• We can't solve yet because we have two time variables, t1 and t2. But we know that t1 will be the same value as t2, because the problems explains that they will be working together from start to finish. The time has to be the same Thus,
  
  t1 = t2
  
  I will substitute in t1 for t2:
  
  t1 * (1/5) + t1 * (1/15) = 1

STEP 5: Solve for t1

• Using some algebra, we get:
  
  t1 = 3.75
  Tada!

DooMer wrote:What is the task? It sounds like person B doesn't know what the fuck hes doing. person A would be the one doing all the work, while person B flops around like a mongaloid and screws shit up.

T=Ammount of 'Work' needed to finish the product.

W(P)='Work' per hour for person P
W(A)= T/5
W(B)= T/15
W(A)+W(B)=T(1/5+1/15)=T(4/15)

How long does it take both to produce an ammount of 'Work' equal to T?

T = x*(W(A)+W(B))= T*x*4/15
<=> 1 = x * 4/15
<=> 15/4 = x

Pext wrote:?

you don't add letters, you add numbers represented by letters.

mjrpes wrote:I'm a bit worried that you said my explanation is convoluted. I hope this is better.

Let X = A's house-building speed, or rate of housebuilding
let Y = B's rate of house building

We define rate of house building as number of houses built per hour

Houses built per house = # of houses divided by time taken

(just like velocity = distance divided by time)

So:

X = A's rate = 1 house divided by 5 hours = 1/5 houses per hour
Y = B's rate = 1 house divided by 15 hourse = 1/15 houses per hour

So combining A's rate and B's rate, we get 1/5 + 1/15 houses per hour:

1/5 + 1/15
= 3/15 + 1/15
= 4/15 houses per hour

Now if the combined rate is 4/15 houses per hour, then how long will it take to build 1 house, or 15/15 houses?

Just as time = distance divided by velocity, time = houses built divided by rate of house building


so time = unknown
houses built = 15/15
rate = 4/15

so time = 15/15 divided by 4/15

15/15 divided by 4/15
= 1 divided by 4/15
= 1 multiplied by 15/4

1/1 * 15/4 = 15/4

15/4 = 3 and three quarters = 3.75 hours

[xeno]Julios wrote:did you short circuit the quadratic by doing that division, thus castrating off one of the two possible solutions (1 and 0)?

mjrpes wrote:Something like that... I got it from another forum. Perhaps a mathematician can explain what happened more clearly.

Nightshade wrote:

[xeno]Julios wrote:did you short circuit the quadratic by doing that division, thus castrating off one of the two possible solutions (1 and 0)?

No, he simply factored (x^2-1) and then ignored that fact that unless you're in a modular number system, 1 cannot equal 0.

Nightshade wrote:

[xeno]Julios wrote:did you short circuit the quadratic by doing that division, thus castrating off one of the two possible solutions (1 and 0)?

No, he simply factored (x^2-1) and then ignored that fact that unless you're in a modular number system, 1 cannot equal 0.

MKJ wrote:

Nightshade wrote:

[xeno]Julios wrote:did you short circuit the quadratic by doing that division, thus castrating off one of the two possible solutions (1 and 0)?

No, he simply factored (x^2-1) and then ignored that fact that unless you're in a modular number system, 1 cannot equal 0.

its like blizzard's 0.999~ == 1 april's fools joke

Pext wrote:

Nightshade wrote:

[xeno]Julios wrote:did you short circuit the quadratic by doing that division, thus castrating off one of the two possible solutions (1 and 0)?

No, he simply factored (x^2-1) and then ignored that fact that unless you're in a modular number system, 1 cannot equal 0.

no... not really.

the 1=0 part only comes by dividing by x-1 = 1-1 = 0

phantasmagoria wrote:

DooMer wrote:What is the task? It sounds like person B doesn't know what the fuck hes doing. person A would be the one doing all the work, while person B flops around like a mongaloid and screws shit up.