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It takes 4 hours for 5 painters to paint a house. How long would it take 9 painters to do the job?

I get confused easily here. Please help me on how to do most of the problem, or at least just tell me how to start off with the problem.

royhaas

05-11-2006, 07:52 AM

It takes 4*5 painter-hours to paint a house.

Mrspi

05-11-2006, 09:58 AM

It takes 4 hours for 5 painters to paint a house. How long would it take 9 painters to do the job?

I get confused easily here. Please help me on how to do most of the problem, or at least just tell me how to start off with the problem.

Can you see that this is an inverse relationship? As the number of painters goes UP, the number of hours goes DOWN.

The basic pattern for an inverse variation is

xy = k

where "k" represents the constant of variation.

Now, suppose we let x = number of painters and y = number of hours. Since it takes 5 painters a total of 4 hours, we can write

5*4 = k

Ok...now you know what k is, so you can write the specific formula for this situation by replacing "k" with the value you got above. And you'll have an equation you can use to find the number of hours required by ANY NUMBER of painters....use the equation to find the number of hours it will take for 9 painters.

TchrWill

05-11-2006, 12:24 PM

It takes 4 hours for 5 painters to paint a house. How long would it take 9 painters to do the job?

I get confused easily here. Please help me on how to do most of the problem, or at least just tell me how to start off with the problem.

The following should give you enough information for solving combined work problems.

If it takes me 2 hours to paint a room and you 3 hours, ow long will it take to paint it together? >>

Method 1:

1--A can paint the house in 5 hours.

2--B can paint the house in 3 hours.

3--A's rate of painting is 1 house per A hours (5 hours) or 1/A (1/5) houses/hour.

4--B's rate of painting is 1 house per B hours (3 hours) or 1/B (1/3) houses/hour.

5--Their combined rate of painting is 1/A + 1/B (1/5 + 1/3) = (A+B)/AB (8/15) houses /hour.

6--Therefore, the time required for both of them to paint the 1 house is 1 house/(A+B)/AB houses/hour = AB/(A+B) = 5(3)/(5+3) = 15/8 hours = 1 hour-52.5 minutes.

Note - T = AB/(A + B), where AB/(A + B) is one half the harmonic mean of the individual times, A and B.

Method 2:

Consider the following diagram -

.........._______________ _________________

..........I B / /\

..........I * / I

..........I * / I

..........Iy * / I

..........I * / I

..........I*****x****** I

..........I / * (c)

..........I(c-y) / * I

..........I / * I

..........I / * I

..........I / * I

..........I / * I

..........I/___________________* ________\/__

A

1--Let c represent the area of the house to be painted.

2--Let A = the number of hours it takes A to paint the house.

3--Let B = the number of hours it takes B to paint the house.

4--A and B start painting at the same point but proceed in opposite directions around the house.

5--Eventually they meet in x hours, each having painted an area proportional to their individual painting rates.

6--A will have painted y square feet and B will have painted (c-y) square feet.

7--From the figure, A/c = x/y or Ay = cx.

8--Similarly, B/c = x/(c-y) or by = bc - cx.

9--From 7 & 8, y = cx/a = (bc - cx)/b from which x = AB/(A+B), one half of the harmonic mean of A and B.

I think this should give you enough of a clue as to how to solve your particular problem.

It takes 4 hours for 5 painters to paint a house. How long would it take 9 painters to do the job?

I get confused easily here. Please help me on how to do most of the problem, or at least just tell me how to start off with the problem.

Can you see that this is an inverse relationship? As the number of painters goes UP, the number of hours goes DOWN.

The basic pattern for an inverse variation is

xy = k

where "k" represents the constant of variation.

Now, suppose we let x = number of painters and y = number of hours. Since it takes 5 painters a total of 4 hours, we can write

5*4 = k

Ok...now you know what k is, so you can write the specific formula for this situation by replacing "k" with the value you got above. And you'll have an equation you can use to find the number of hours required by ANY NUMBER of painters....use the equation to find the number of hours it will take for 9 painters.

So.... 5*4=20, so the equation to solve is 9*y=20... The answer I got was 2.2. Is it correct?!?

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