Solve Word Problem: 30 Persons in 4 Days = 40 Persons in x Days

[alijan kk]

A task is completed by 30 persons in 4 days. In how many days, the same will be completed by 40 persons ?

My attempt:
(30/4)/1=(40/x)/1

(30 persons per 4 days per task=40 persons per x days per task)

Doing this way i found x= 5.33 day or 5 whole days .

is this correct way of doing this problem?

 

[berkeman]

A task is completed by 30 persons in 4 days. In how many days, the same will be completed by 40 persons ?

My attempt:
(30/4)/1=(40/x)/1

(30 persons per 4 days per task=40 persons per x days per task)

Doing this way i found x= 5.33 day or 5 whole days .

is this correct way of doing this problem?

Why would it take longer with more people working in it? Always sanity-check your answers to see if something doesn't look right...

BTW, I will move this to the schoolwork forums for you now.

 

[PeroK]

A task is completed by 30 persons in 4 days. In how many days, the same will be completed by 40 persons ?

My attempt:
(30/4)/1=(40/x)/1

(30 persons per 4 days per task=40 persons per x days per task)

Doing this way i found x= 5.33 day or 5 whole days .

is this correct way of doing this problem?

What about if there is only 1 person? By your method, $x = 4/30$ days, which is about an hour!

 

[RPinPA]

You want to get it down to what each person is contributing. Then you can work with a different number of people.

A task is completed by 30 persons in 4 days.

So how much do those same 30 people do in 1 day? How much of the 4-day job is done after day 1?

Once you know that, how much does each person do in 1 day?

 

[Nimol]

Try this!
Let’s say you alone can finish a task in two days. So if you get help from one of your friends, that task will be finished in only one day. How about four people working together? It would remain only (1/2)day. You see, the amount of days is reduced as the people increases. This case is opposite from your attempt.

 

[archaic]

As others have said, it doesn't seem logical that more people take more time to do the task. For these cases where a variable decreases when the other increases we say that they are inversely proportional.
Have a look at this functions, $f(x) = \frac{6}{x}$, try increasing the values of $x$ and you will notice that $f(x)$ will decrease as you do so.
In your exercise, $persons$ and $days$ are inversely proportional which means that $days=\frac{k}{persons}$ where $k$ is a constant.
You already have two values, I let you do the rest ;)

 

[symbolipoint]

The question is a constant-rates problem or exercise. Two parts in it. Descriptive part, and question part using different number of workers.

R=W/T
RATE of work is amount of work W divided by time T.
This can easily also be stated RT=W.

If all workers each work at the same rate, then R is the work rate for 1 worker, and for N workers, the algebraic formula is NRT=W.

Let's see how this goes:

A task is completed by 30 persons in 4 days. In how many days, the same will be completed by 40 persons ?

The first sentence let's us say:
30r*4=1

The "1" is for those thirty persons doing ONE TASK.

The question, second sentence, let's us say:
40*r*x=1

r being the work rate of anyone person, x the number of days to do the ONE TASK.

You should be able to finish from there.