help me with a algebra problem?

Question

Suppose one painter can paint an entire house in twelve hours, and the second painter takes eight hours. How long would it take the two painters to paint the house together?

1. Work:: ______ x Rate:: ______ = Work Done:: ____
2. Work:: ______ x Rate:: ______ = Work Done:: ____


Answer: ___________

does that make sense???
on my worksheet it has it in boxes but I'll try doing it in boxes if it helps.

here's the link
http://i8.tinypic.com/8b97h2b.jpg

Answer 1

They'll paint it in 10 hours.

Here's why:

If it's the same house, you can just find the average of their times, which is the sum of the times the workers take to paint the house, divided by the number of workers. So

Worker 1: 12 hours
Worker 2: 8 hours.

# of workers: 2

So, (12 + 8) ÷ 2 = 20 ÷ 2 = 10.

If they work together, they will get the house done in 10 hours.

Hope I helped!

Answer 2

Let's see.....

Obviously, the second painter paints more of the house, because (s)he paints it faster. How about we call the whole house as 1. The 1st painter paints 1/12 of it in 1 hour, and the second one paints 1/8 of it in 1 hr.

After both have painted for 1 hour, 20/96 is done, or 5/24.
After 2 hours, 10/24 is finished.
After 3 hours, 15/24 is finished.
After 4 hours, 20/24 is finished.

As you see, the rate for P1 is 1/12 per hour, and P2 is 1/8 per hour. now, just 1/6 is left, or 16/96. 1 min is 1/720 + 1/480 = 5/1440. 1/6 / 5/1440 = 1/6 x 1440/5 = 1440/30 = 48 min.

Now, the answer is that it takes 4 hours and 48 minutes for both to paint the whole house. Or it takes 4 4/5 hours.

Hope it helps!!!!!!!!

P.S. I don't know if they painted non-stop, so I'm 99.9999999...% confident. =-)

Answer 3

x / 12 + x / 8 = 1

Multiply both sides of the equation by 24

24(x/12) + 24(x/8) = 24(1)

2x + 3x = 24

5x = 24

Divide both sides of the equation by 5

5x / 5 = 24 / 5

x = 24/5

x = 4 4/5 hours
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Find the minlutes

Multiiply 4/5 times 60

4/5(60) =

240/5 = 48. . .←. .Minutes

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They can paint the entire house is 4 hours and 48 minutes or 4' 48"

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Answer 4

If they painted two different houses, it takes 20 hours total.
So together, on average, it'll take 10 hours.

Answer 5

I don't know about using your boxes but the way you solve this kind of problem is as follows:

Painter 1 can paint 1/12 of a house in 1 hour.
Painter 2 can paint 1/8 of a house in 1 hour.
Together they can paint (1/12 + 1/8) = 5/24 of a house in 1 hour.
That means it will take them 24/5 = 4.8 hours to paint the house working together.