Painter problem: How many more days are required?

[Vettester]

So there are 3 of us here scratching our heads on this one:

A painting job can be completed by 7 painters in 24 days. If 28 more painters join the team 9 days after starting work on the job, then how many more days are required to complete the job?

So what we tried to answer was "In 9 days, how far did the 7 painters get?" We came up with 37.5% complete done in 9 days: 9/24 = 0.375, or 37.5%. That leaves 62.5% of the job remaining. At that time there are 28 more painters for a total of 35 painters working. That is 5x the amount of painters, with 62.5% remaining.

We need to find out how many days 1 painter would take. We tried:

7x24 = 168 days.
168 days divide 35 total painters after 9 days:
168/35 = 4.8 days to complete.
4.8 days multiply the 62.5% remaining.

That leaves 3 days. So the 7 workers completed 37.5% in 9 days, and 35 workers finished up in 3 days. So in our whole mess, we came up with: 3 more days.

We all think this is the correct answer. If we are off or there is an easier way to calculate this, we would much appreciate it.

 

[arthur ohlsten]

3 more days is correct
let R be the rate 7 painters paint at , and P be the amount to be painted
P/R= 24days

after 9 days there is 15/24 of the job left, or .625 P left to do
the rate of 7 painters plus 28 painters = 7R+4R

.625P/[4R+5R]=x
but P = 24R, substitute
.625[24R] / [5R] =x
x=3 days answer

Arthur

 

[Denis]

Same as:
A painting job can be completed by 1 painter in 24 days. If 4 more painters join the team 9 days after starting work on the job, then how many more days are required to complete the job?

Per day: 1/24 of job is done; so:
after 9 days: 1 - 9/24 = 15/24 = 5/8 of job is left

Now, per day: 5/24 of job is done; so:
(5/8) / (5/24) = 3 days required

 

[stapel]

A painting job can be completed by 7 painters in 24 days. If 28 more painters join the team 9 days after starting work on the job, then how many more days are required to complete the job?

Seven guys and twenty-four days is (7 guys)(24 days) = 168 man-days. (This is just like "man-hours" the auto shop uses to bill you for the work they do on your car.)

Assuming "the team" is seven guys (this is not stated), then:

. . . . .(7 guys)(9 days) = 63 man-days

The job requires a total of 168 man-days, so there are 168 - 63 = 105 man-days remaining. With a total of 28 + 7 = 35 guys, you then have:

. . . . .(105 man-days) / (35 guys) = 3 days

Easy-peasy.

Eliz.