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Well, this is on my final exam review, and it's the only one I can't do and get an answer. The answer guide says it's supposed to equal out into 8.53 hours.
You may have to use the quadratic equation, I'm not sure.
X = -b +/- (square root(b^2-4ac
---------------------------------------------
2a
Bill and his son Billy can clean the house together in 4 hours. When the son works alone, it takes him an hour longer to clean than it takes his dad alone. Find how long to the nearest hundreth of an hour it takes the son to clean alone?
I thought I was going to get it by doing fractions, cancelling out the denominator, and making it into a quafratic, but it didn't work.
Any math people out there??? I would greatly appreciate it.
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-Charles Bukowski
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Quote:
Bill and his son Billy can clean the house together in 4 hours. When the son works alone, it takes him an hour longer to clean than it takes his dad alone. Find how long to the nearest hundreth of an hour it takes the son to clean alone?
the answer is $ 25.00.....Bill & billy hired a maid...sorry I stink at math...& spelling...and......
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I got it started like this,
1/4 +1/x+1 = 1/x
I tried to do the common denominator cancelling, I did and even set it up it X^2 +bx +c from and it didn't work either.
Anyone??? Please help, I will give you a money reward.
Find what you love and let it kill you.
-Charles Bukowski
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Legend
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What did you assign as the variables?
I am unfamiliar with this feeling of optimism
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Wow, I'm sorry I messed up in my original post.
Together time= 4 hours
Dad's time = x
Son's time= x+1, because it takes him one hour longer
Find what you love and let it kill you.
-Charles Bukowski
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I can feel my blood pressure rising. I emailed it to my wife who is a lot better at math than I am. I'll let you know if she gets back to me. If you figure it out, post it. I'm curious now.
I am unfamiliar with this feeling of optimism
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I'm going to my college right now, it like right next door. They do have a math help class that starts at 3PM, I'll let you know the answer. 
Find what you love and let it kill you.
-Charles Bukowski
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Legend
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The better question is: How long does it take mom to reclean the house when she gets home because Bill and Billy didn't do it right? 
yebat' Putin
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Quote:
The better question is: How long does it take mom to reclean the house when she gets home because Bill and Billy didn't do it right?
No DC, the better question is, why was Mom out of the house to begin with? 
I am unfamiliar with this feeling of optimism
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In that case, based on extensive life experience, I would say that X must equal 4.
Dad takes 4 hours.
Kid takes 5 hours.
Together takes 4 hours because Dad has to slow down every now and again to tell Kid to stop screwing around and get back to work.
Browns is the Browns
... there goes Joe Thomas, the best there ever was in this game.
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The problem I see is that the equation is "assuming" something. That the amount of time it would take to clean independently is directly relative to the time it takes 2 people to clean.
Basically assuming it would take 1 person 8 hrs if cleaning alone as a base. In a real world that is not true.
We don't have to agree with each other, to respect each others opinion.
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Ok, so it takes the dad x time, and the son x+1 time.
Another way of saying this is that the amount of work the dad will do in x time, the son will do in x+1 time, so in one hour, the dad will do 1/x of the work, and the son will do 1/(x+1) of the work
We want the total amount of work done to be 1 (the whole job), we know, they can both do it in 4 hours:
4(1/x+1/(x+1)) = 1
Solve that equation out for x, and then you can plug the x+1 value for his son and get that to equal 1.
~Lyuokdea
Last edited by Lyuokdea; 03/13/08 02:40 PM.
"When a foreigner resides among you in your land, do not mistreat them. The foreigner residing among you must be treated as your native-born. Love them as yourself, for you were foreigners in Egypt. I am the LORD your God." Leviticus 19:33-34
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Quote:
Ok, so it takes the dad x time, and the son x+1 time.
Another way of saying this is that the amount of work the dad will do in x time, the son will do in x+1 time, so in one hour, the dad will do 1/x of the work, and the son will do 1/(x+1) of the work
We want the total amount of work done to be 1 (the whole job), we know, they can both do it in 4 hours:
4(1/x+1/(x+1)) = 1
Solve that equation out for x, and then you can plug the x+1 value for his son and get that to equal 1.
~Lyuokdea
Just reading that reminded me why I hated math!
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Quote:
4(1/x+1/(x+1)) = 1
Yeah, I double checked the math ... he's right. That's your equation. Oi! Now I remember why I didn't go for the math minor in college when all I had to do was take one more class.
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I'm going back to the "women stuck on toilet seat" thread.
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I'm going back to the "women stuck on toilet seat" thread.
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I understand her staying on a toilet for two years better than I understand what's being discussed here.
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I don't know. We haven't learned this quite yet. 
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Quote:
4(1/x+1/(x+1)) = 1
I just realized that might not read correctly ...
with parens ... it's:
4 * ( (1/x) + (1/(x+1)) ) = 1
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Quote:
Quote:
4(1/x+1/(x+1)) = 1
I just realized that might not read correctly ...
with parens ... it's:
4 * ( (1/x) + (1/(x+1)) ) = 1
A lot of people were wondering.... 
yebat' Putin
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Shouldn't you be sharpening your stick or something? 
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right, that's what mine reads I believe, though i guess the 1/x can be somewhat ambiguous.
~Lyuokdea
"When a foreigner resides among you in your land, do not mistreat them. The foreigner residing among you must be treated as your native-born. Love them as yourself, for you were foreigners in Egypt. I am the LORD your God." Leviticus 19:33-34
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You can always ask your proffesor when will you ever use this in life.
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I don't like the answer the guide gave you -- it doesn't seem to make any sense that it would take Billy 8.53 hours to a job that his Dad does in 7.53, and it takes them both 4 hours,...????? Seems something is missing,...like the rate they both work AT,.... So I did it like this,....since they supposedly did this together, they each did exactly half of the work. That's probably incorrect from the start, since Dad apparently has more work ethic,.... . But, assuming they each did half, and together it equals four hours, then X (Dad's time) plus X + 1 (Billy's time) multiplied by 1/2 (amount of work done by each) equals 4 hours. 1/2 (x+x+1) = 4 Multiply both sides by 2 x+x+1=8 Subtract 1 from both sides 2x = 7 x = 3.5 Dad's work time x+1 = 4.5 Billy's This would mean Billy is a dirtbag,......
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Here it is, it's kind of hard to write it because there's not math symbols on the keyboard, but here it goes. 1/x+1 + 1/x=1/4 You do commong denominators cancelling, and mulitply by every term: (4x)(x+1) is the commong denominator, therefore after cancelling, you're left with 4x+4(x+1)=x(x+1) 4x+4x+4=x^2+X 8X+4=x^2+X -8x -8x(doing this to both sides) 4=x^2-7x-4(you then need ot get it in standard X^2+bx+c form for the quadratic equation) 0=x^2-7x-4(We now need to start the quadratic equation and set it up) A=1 B=-7 C=-4 The easiest way is to find the discriminate first, so, b^2-4ac, and plug you numbers in. (-7)^2-4(1)(-4)=65 x=7 +_(plus or minus) (square root)(65) -------------------------------------------------------- 2(1) x=7+(square root)(65) ------------------------------- 2 You now solve, so 7, plus the square root of 65=15.06225775 now, you divide by 2, which equals, 7.53, BUT this is not the answer. You have to remember the question is asking for how long it takes the SON to clean. Therefore, it would be 7.53+1=8.53. FINAL ANSWER=By himself it takes the son a total of 8.53 hours to clean the house alone. As FloridaFan pointed out, this is completely untrue and also false, a person would never take 8 or more hours to clean the house. Now just think, you did all that for 8.53! Wow, not very gratifying. But I'm glad I've convinced you all that math is evil, you must hate it, loathe it, and fear it. 
Find what you love and let it kill you.
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My first response is bogus, but I got 8.5 another way without the quadratic formula,....
Assuming the amount of work both could do was equal, they did 8 hours of work.
So, since Billy takes "plus one" more time than Dad, i.e, x+1, then x+x+1 = 16, meaning x = 7.5,...Billy 8.5.
That does make sense to me now,.....
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correct.
And Oohrah, that's a good way to approximate the correct answer, which is the first method of getting the right answer. You'll notice what you did is slightly wrong though, because you just assume that the both did an equal amount of work, while in fact the father will do slightly more than half the work, and the son will do slightly less.
Edit: Of course, getting within 1% of the correct answer in 1 minute, is sometimes much better than getting the right answer in 100 minutes.
~Lyuokdea
Last edited by Lyuokdea; 03/13/08 05:52 PM.
"When a foreigner resides among you in your land, do not mistreat them. The foreigner residing among you must be treated as your native-born. Love them as yourself, for you were foreigners in Egypt. I am the LORD your God." Leviticus 19:33-34
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Math isn't evil ... women are. .gif) 
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Quote:
My first response is bogus, but I got 8.5 another way without the quadratic formula,....
Assuming the amount of work both could do was equal, they did 8 hours of work.
So, since Billy takes "plus one" more time than Dad, i.e, x+1, then x+x+1 = 16, meaning x = 7.5,...Billy 8.5.
That does make sense to me now,.....
That's where you are going wrong. Dad isn't doing half the work and stopping while he waits for Billy to finish. After Dad finishes his half ... he's cutting into the workload that Billy has left until they both finish.
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For all we know Billy is texting his girlfriend for 3 hrs while dad does most of the work? So the two of them putting in 4 hours is dad = 3x and billy = 1x Like I said before, this word problem is "assuming" alot. So if it is me, I'm going the honest answer. Bill and Billy don't clean, Bill is married to Barbara who does the cooking and cleaning, and it's Saturday dammit, Bill and Billy are too busy watching the college ball games to be cleaning the damn house, it looks fine as it is.
We don't have to agree with each other, to respect each others opinion.
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Quote:
correct.
And Oohrah, that's a good way to approximate the correct answer, which is the first method of getting the right answer. You'll notice what you did is slightly wrong though, because you just assume that the both did an equal amount of work, while in fact the father will do slightly more than half the work, and the son will do slightly less.
Edit: Of course, getting within 1% of the correct answer in 1 minute, is sometimes much better than getting the right answer in 100 minutes.
~Lyuokdea
Thanks for the props,.... What still bugs me is the difference in their real rates of work,...????
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Maybe Billy does a better, more careful job than Bill.
#gmstrong #gmlapdance
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So let me see if I get what I'm reading right.... GIRLS = EVIL 2 MONEY = EVIL So with that one can determine if you use money to buy a girl our formula would look like this GIRLS = MONEY......SO BUYING A HOOKER ONE CAN ASSUME THERES NO NEGATIVE OR POSITIVE OUT COME SENCE THERE BOTH EQUAL. I like math.....
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