math

[stocktroll]

how do i solve this?:
it takes person A 5 hours to do task.
it takes person B 15 hours to do task.

how long will it take to do task together?

[SOAPboy]

10 hours..

Id assume anyways.. id "figure" its 5+15/2=10

Dunno tho, i suck at math

[Postal]

Figure out the percentage of project they can do per hour individually, (1project/5hours and 1project/15hours) and add them until you reach 100%?

Hour-------1----------2-----------3--------------4
Person A--20%------40%------60%----------80%
Person B--6.5%-----13%------19.5%--------26%
Total-------26.5%---53%-------79.5%--------106%

1/15 is around 6.6666%

Project got done at around 3h45m?

I could be totally wrong though, I never do any problems like that.


edit: 54 wtf

[Bdw3]

Edit: damnit poostal.... :icon33:


A bit less than 4 hours

[SOAPboy]

Yeah i was way off.. lmfao

[Postal]

: )

[DooMer]

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.

[stocktroll]

Yeah i was way off.. lmfao

not only were you way off but your answer made absolutely no sense. Why would the length increase 2 fold from what one person could do by themselves?

[mjrpes]

person a: 1x = 5 (takes 5 hours to get 1 task done)
person b: 1x = 15 (takes 15 hours to get 1 task done)

algebra:

x/5 = 1
x/15 = 1

together, to complete one task, the equation is

x/5 + x/15 = 1

3x/15 + x/15 = 1 (common denominator)

3x + x = 15 (multiply both side)

4x = 15

x = 15/4 = 3.75 hours

[[xeno]Julios]

well imagine it took A 5 hours to build 1 house and B 5 hours to build one house.

How long would it take them both to build one house?

With the addition of B, we have double the efficiency of A, so it'll take half the time (2.5 hours).

How can we arrive at this number mathematically?

let A's time = 5 hours = x
let B's time = 5 hours = y
let AB's time = z

how can we manipulate the number 5 to reach 2.5 (which we know intuitively is the correct answer)?

We divide by 2.

What can we do with x and y to make 2?

how about 5 divided by 5, added to 1

so x/y + 1 = 2.

why would this make intuitive sense though? On the surface it seems arbitrary.

well the combined efficiency would be the efficiency contributed by B, added to the A

so if be was 20% as efficient as A, we'd have 1 + 0.2

(this is sort of a botched explanation but work with me - i'm flying on the seat of my pants here!)

so if x = 5 and y = 15, we have z = 1+ 5/15 = 1.33333333

so i'm guessing the answer is 5 hours divided by 1 and a third which is 3.75

which is exactly what postal got

3 hours and three quarters

3:45

[[xeno]Julios]

fuck mjrpes beat me in simplicity and time

[mjrpes]

QED FTW!!!

[stocktroll]

person a: 1x = 5 (takes 5 hours to get 1 task done)
person b: 1x = 15 (takes 15 hours to get 1 task done)

algebra:

x/5 = 1
x/15 = 1

together, to complete one task, the equation is

x/5 + x/15 = 1

3x/15 + x/15 = 1 (common denominator)

3x + x = 15 (multiply both side)

4x = 15

x = 15/4 = 3.75 hours

bah i just came up with that equation but thanks for the verification. But sadly thats just the easy part... now i have to explain it to a plant.

[[xeno]Julios]

person a: 1x = 5 (takes 5 hours to get 1 task done)
person b: 1x = 15 (takes 15 hours to get 1 task done)

algebra:

x/5 = 1
x/15 = 1

together, to complete one task, the equation is

x/5 + x/15 = 1

bah i'm confused - if x/5 = 1 and x/15 = 1, then x/5 + x/15 = 2 right?

[mjrpes]

no no... that's would be saying how much time does it take for both to work together to get '2' tasks done.

[mjrpes]

the problem is the first step... 1x =5 , 1x = 15. it's not proberly formulated and I don't know how to do it.

[[xeno]Julios]

now i'm really confused - what does x mean in your equations??

[mjrpes]

I don't know

[[xeno]Julios]

i like my explanation better!

[mjrpes]

I tried reading your explanation and got lost a bit... I will have to take two excedrin and give it a shot in about half hour.

[[xeno]Julios]

Ok let's use a velocity metaphor, where distance is the number of houses built, time is the time it takes to build it, and velocity is the rate of house building.

(gotta go for a while - bbl)


will continue when i get back if nobody's picked up this thought


i think key is to quantify the efficiency of each using their "velocity"

houses per unit time

standard units - then easy to combine

[mjrpes]

Let's try starting with this:

(a) x/5 = y

(b) x/15 = y

Where each equation stands for the efficiency of each worker: x is a variable that stands for the amount of hours put in, and y stands for the number of tasks to complete. Let's plug in 1 for the number of tasks to complete:

(a) x/5 = 1

(b) x/15 = 1

Solving for x, we see it takes 5 hours for worker A to get one task done, and 15 hours for worker B to get a task done. Now let's go on to finding the equation that expresses their work efficiency to get one task done:

(c) x/5 + x/15 = 1

From here, use algebra to solve, and you get 3.75 hours in result.

[[xeno]Julios]

snip

there's something fundamentally wrong with this formulation: there is an inconsistency in the equations you set out.

a) x/5 = y

(b) x/15 = y

this is as logical as saying 1 = 2

(c) x/5 + x/15 = 1

From here, use algebra to solve, and you get 3.75 hours in result.

If we use algebra to solve we get
2x + 20 = 1
2x = -19
x = -9.5


We need to define efficieny in quantitative terms:

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:

A's rate = 1 house divided by 5 hours = 1/5 houses per hour
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

[mjrpes]

This might be a little more clearer:

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. For worker A,

1 task = 5 hours
1/5 tasks per hour = e (for worker A)

For worker B,

1 task = 15 hours
1/15 tasks per hour = e (for worker B)

We can substitude the efficiency back into our original equations:

x * (1/5) = A
x * (1/15) = B

Simplified:

x/5 = A
x/15 = B

Now let's go on to finding the equation that expresses the amount of work done for a certain amount of tasks, if both work together:

A + B = t

Where t stands for the total number of tasks needed to complete. We know that t=1, so we now have,

A + B = 1

Now we can go and substitute in

(x/5) + (x/15) = 1

From here, use algebra to solve:

(3x/15) + (x/15) = 1
3x + x = 15
4x = 15
x = 3.75 hours

[mjrpes]

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