Answer: 4 workers
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Step-by-step explanation:
We have 9 workers painting walls in a house. Let's say the total square feet needed to be painted is 9000 square feet. I picked some arbitrary large multiple of 9, so that it leads to 9000/9 = 1000 square feet per worker.
In other words, each worker paints 1000 square feet.
They can do the job in 48 hours, which means their rate is 1000/48 = 125/6 square feet per hour approximately.
After 8 hours, each worker paints 8*(125/6) = 500/3 square feet. So all 9 workers painted 9*(500/3) = 1500 square feet
Put another way: they got 8/48 = 1/6 of the job done after 8 hours, so (1/6)*9000 = 1500 sq feet of wall has been painted so far. This leaves 9000-1500 = 7500 sq ft unpainted.
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Let x be the number of workers that leave.
There are 9-x people still on the job.
The 7500 sq ft of left over wall is divided among the 9-x people. Each worker gets 7500/(9-x) sq feet of wall to paint.
Earlier we found each worker's rate was 125/6 sq ft per hour. If they complete the remaining job in 72 hours, then,
(rate)*(time) = (amount of job done)
(125/6)*(72) = 7500/(9-x)
1500 = 7500/(9-x)
1500(9-x) = 7500
9-x = 7500/1500
9-x = 5
-x = 5-9
-x = -4
x = 4
4 workers went home.
If 4 workers went home, then 9-4 = 5 workers remain
They each have 7500/5 = 1500 sq ft of wall to paint, which helps confirm the answer.