A group of 9 workers was assigned to paint the walls in a house, which could be completed in 48 hours. However, after working 8 hours, some of the workers left the group and the remaining workers could complete the job in 72 hours. How many workers left the team? Plz write equation:0

4 workers

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.

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.

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