1. Grade 9 Algebra - 2 Work Problems

I have two quadratic work problems that I REALLY need help with. It would be great if someone could supply some help relativly soon if possible.

1. Working alone, Colleen can paint a house in 2 hours less than James. Working together, they can paint the house in 10 hours. How long would it take James to paint the house by himself?

2. Together, Maria and Johannes can pick a bushel of apples in 16 minutes. Maria takes 4 minutes more to pick a bushel than Johannes does. Find the time it takes each person to pick a bushel of apples alone.

Thank you!

2. Could you explain how you did those? I tried doing it with the formula that my teacher gave me (time (rate 1 + rate 2) = job still to do) but I was getting all sorts of weird answers, not simple ones like you ended up with.

Edit: I checked the back of my textbook, and it said the answers were Maria= 34.1 minutes and Johannes= 30.1 minutes. But I have no idea how it got those answers.

3. I was just wondering if there were any sort of steps in between that you didn't put down, but I figured out how you did it myself after I had posted that. The problem is, the book said the answers are 34.1 for Maria and 30.1 for Johannes in the second problem, but I don't understand how to get those.

4. Darn, i am so wrong! They should take MORE time if they do it seperately! Ill fix it. Sorry.

5. This is how I did the second problem:

Johannes's rate is 1/x. Maria's rate is 1/(x+4).

The formula I used was 16 ( 1/x + 1/(x+4) ) = 1

Then I simplified it and got (16(2x + 4)) /x(x+4) = 1

Then I distributed in the 16: 32x +64/x(x+4) =1

But I don't know if that whole thing was right up to there, and I don't know what to do next.

6. Originally Posted by SwissArmelle
This is how I did the second problem:

Johannes's rate is 1/x. Maria's rate is 1/(x+4).

The formula I used was 16 ( 1/x + 1/(x+4) ) = 1

Then I simplified it and got (16(2x + 4)) /x(x+4) = 1

Then I distributed in the 16: 32x +64/x(x+4) =1

But I don't know if that whole thing was right up to there, and I don't know what to do next.
My final formula is:
$\displaystyle x^2 - 28x + 64 = 0$

And then x = 25,49 or x = 2,51

Now set it back into your original equation

7. Hmm...that makes sense. But then how do you factor it? I tried a bunch of different combinations but none of them worked. Do I have to just use the quadratic formula?

8. Yes you will just have to do the quadratic formula. Sorry for my mistake, but i did these problems 4 years ago

9. Okay, I did the quadratic for the second problem and got the same answers as you...I guess the book is just wrong. Did you try the first one, by any chance? I got 10 plus or minus radical 101.

10. Do you understand SwissArmelle?

11. Originally Posted by janvdl

They paint 1 house in 10 hours...

$\displaystyle 10(\frac{1}{x} + \frac{1}{x+2}) = 1$

$\displaystyle 0 = 10x^2 + 18x - 2$
Do you think you could show me how you got from the first one to the second one? were there any middle steps? I just want to understand exactly how you did that.

12. Originally Posted by SwissArmelle
Do you think you could show me how you got from the first one to the second one? were there any middle steps? I just want to understand exactly how you did that.
I keep making silly mistakes. Right, lets go through this together.

$\displaystyle 10( \frac{1}{x} + \frac{1}{x-2}) = 1$

$\displaystyle \frac{1}{x} + \frac{1}{x-2} = \frac{1}{10}$

Multiply through with $\displaystyle x^2 - 2x$

$\displaystyle x - 2 + x = \frac{x^2 - 2x}{10}$

Multiply through with $\displaystyle 10$

$\displaystyle 20x - 20 = x^2 - 2x$

$\displaystyle 0 = x^2 + 2x - 20x + 20$

$\displaystyle 0 = x^2 + -18x + 20$