Quick help on an easy solve.

[Fmedina1992]

Ok before i post the math problem i have already solved it im positive but i need the equation for how it should be solved.

If 6 workers complete 8 tasks in 4 hours how many workers would it take to complete 12 tasks in 2 hours. My answer is 15.

The way i solved it was by adding 6 more workers to the first problem reducing the completion time to 2 hours then if i add the 4 to 8 which is only half the original task load to keep the hours at 2 i only needed to add half of the amount of workers to the 12 making it 15. If im wrong please help i just need the equation itself thank you very much

 

[Cubist]

Sorry, 15 isn't right.

Why don't you start by writing an equation that calculates how many tasks that one person can complete in one hour...

p = ??

State your variables, perhaps w=number of workers, t=time in hours, n=number of tasks

(p might be a fraction, that's OK)

Then you can use that equation twice:- once for the given scenario; and once for the second scenario.

 

[Romsek]

The rigorous way to solve this is to use rates. The rate we want is worker hours per task.
Knowing the units we can immediately write

\(\displaystyle rate = \dfrac{6~worker \cdot 4~hr}{8~task}=3 \dfrac{worker\cdot hr}{task}\)

Having found this we apply it as

\(\displaystyle 3 = \dfrac{W \cdot 2}{12}\\
W=18
\)

It takes 18 workers to complete 12 tasks in 2 hrs.

Your method wasn't totally incorrect. We can do the following.

6 workers 4 hrs for 8 tasks is equivalent to 6 workers 2 hrs for 4 tasks
This is equivalent to 18 workers 2 hrs for 12 tasks.

 

[Cubist]

The rigorous way to solve this is to use rates. The rate we want is worker hours per task.
Knowing the units we can immediately write

\(\displaystyle rate = \dfrac{6~worker \cdot 4~hr}{8~task}=3 \dfrac{worker\cdot hr}{task}\)

I think it's easier to think in terms of productivity, or rate of output, as a quantity that increases if the number of tasks completed goes up while the time and number of workers stay constant. Your version of rate would decrease in these circumstances.

 

[Cubist]

Fmedina1992,

In case my comment above has confused you, then I'd recommend following any advice/ examples that your teacher has given.

If they have used the term "worker hours per task" anywhere then you can use Romsek's calculations, they are correct.

If your notes say "productivity", or "rate of output", or "tasks per worker hour" then you just need to flip most of the fractions of Romsek upside down. Basically the 3 worker hours per task becomes [math]\frac{1}{3}[/math] of a task per worker hour. The final answer comes out exactly the same, 18 !

It's just two ways of reaching the same goal.

 

[Dr.Peterson]

Ok before i post the math problem i have already solved it im positive but i need the equation for how it should be solved.

If 6 workers complete 8 tasks in 4 hours how many workers would it take to complete 12 tasks in 2 hours. My answer is 15.

I think the important thing here (apart from your work being wrong) is that there is no such thing as "the equation", and there is no "how it should be solved". There are many ways to solve such a problem, not all of which need an equation at all, and many of which need only an expression, not an equation.

You will have to tell us what method you were taught, and exactly what the assignment said you had to do. If it doesn't mention an equation, then you don't need one!

 

[Fmedina1992]

This was actually a brain training question im just trying to brush up on my math skills is all. So this isnt homework. Im merely trying to remember how to solve certain problems.

 

[Fmedina1992]

The rigorous way to solve this is to use rates. The rate we want is worker hours per task.
Knowing the units we can immediately write

\(\displaystyle rate = \dfrac{6~worker \cdot 4~hr}{8~task}=3 \dfrac{worker\cdot hr}{task}\)

Having found this we apply it as

\(\displaystyle 3 = \dfrac{W \cdot 2}{12}\\
W=18
\)

It takes 18 workers to complete 12 tasks in 2 hrs.

Your method wasn't totally incorrect. We can do the following.

6 workers 4 hrs for 8 tasks is equivalent to 6 workers 2 hrs for 4 tasks
This is equivalent to 18 workers 2 hrs for 12 tasks.

Thanks i see what i did wrong with my version when i added 6 workers to the already 6 completeting the 8 tasks to make it 2 hours when i added 4 more task instead of adding 3 more workers i needed to add 6 more. Man i feel like i dope.