Find the Time to Complete a Painting Job with Proportion Homework Help

[LiHJ]

Homework Statement

Dear Helpers,
This is the question:

It takes 30 days for 6 trained workers to complete a painting job. The same painting job can also be completed in 30 days by a group of 10 untrained workers. How long would a group of 4 untrained and 4 trained workers to complete the same painting job?

Homework Equations

The Attempt at a Solution

This is my working:

Rate of working based on 30 days (Trained)= (1/6)
Rate of working based on 30 days (Trained)= (1/10)
Combined rate of working based on 30 days = (1/6)+(1/10)=(4/15)

Amount of work done by 4 set of (1 Untrained + 1 trained) workers express in fraction=
(4/15) x 4=(16/15)

(16/15) -----30days
1 whole ------ 30 x (15/16)=28.125

therefore answer = 29 days

Is my working logical or can be better?

Thank you

 

[HallsofIvy]

Why talk about "based on 30 days" when the problem is asking you to find the number of days the job will take?

If it takes 6 trained workers to do the job in 30 days, then each trained worker is doing 1/6(30)= 1/180 job per day. If it takes 10 untrained workers 30 days to do the job then each untrained worker is doing 1/10(30)= 1/300 job per day. So 4 trained and 4 untrained workers will do 4/180+ 4/300= 1/45+ 1/75= ? jobs per day.

 

[Redbelly98]

The answer should not depend on what units you choose to express time in. We are free to express the rates as "per day", "per week", or "per 30 days" as the OP essentially did. Working in units of 30 days should and did get to the right answer.

Homework Statement

Dear Helpers,
This is the question:

It takes 30 days for 6 trained workers to complete a painting job. The same painting job can also be completed in 30 days by a group of 10 untrained workers. How long would a group of 4 untrained and 4 trained workers to complete the same painting job?

Homework Equations

The Attempt at a Solution

This is my working:

Rate of working based on 30 days (Trained)= (1/6)
Rate of working based on 30 days (Trained)= (1/10)
Combined rate of working based on 30 days = (1/6)+(1/10)=(4/15)

For clarity I would mention right here that this is the rate for 1 untrained + 1 trained worker. Otherwise the reader (or person grading your work) wonders at this point just what rate you are talking about -- even though you do mention "(1 Untrained + 1 trained) workers" later on.

Amount of work done by 4 set of (1 Untrained + 1 trained) workers express in fraction=
(4/15) x 4=(16/15)

(16/15) -----30days
1 whole ------ 30 x (15/16)=28.125

therefore answer = 29 days

Is my working logical or can be better?

For a math class problem, I would leave the answer as 28.125 and not round up to 29 days.

Also -- it may be that your teacher is fine with setting up the relation as you did:

(16/15) -----30days
etc.​

But I prefer to make an explicit equation involving the three quanties, "Complete Jobs", "Rate", and "Time":

[Complete Jobs] = [Rate]·[Time]​

or

J=R·T​

We want the time to do 1 complete job, so J=1, and you already calculated the rate as 16/15. Solve for T, and realize this value is the number of 30-day periods to complete the job.

But that's just my personal preference; if your teacher uses your setup when working examples in class, what you did should be fine.

 

[LiHJ]

Thank you for reading and clearing my doubts about the question.