Help me set up an algebra equation.

(BTW, I spit on the grave of whoever invented this crap.)

Suppose that Hortense and Mort can clean their entire house in 7 hours, while their toddler, Mimi, just by being around, can completely mess it up in only 2 hours. If Hortense and Mort clean the house while Mimi is at her grandma's, and then start cleaning up after Mimi the minute she gets home, how long does it take from the time Mimi gets home until the whole place is a shambles?

:silly:

This is not only a bad problem it is a horrible problem...are you saying the unknown is how long Mimi stayed at grandams? This is not a good problem for algebra nor homemakers???

Algebra was invented by arabs, and dissin' the arabs makes chimpy smile.

let x be a dirty house. it takes 2 hours to dirty it, so x/2, and 7 hours to clean it, so x/7.

x/2 - x/7 = 1

7x - 2x = 14

x = 14/5

it takes the little rat almost three hours to wreck the place.

It is 2-4/5 hours. I just have to be able to form the equation to get that answer.

all during this trashing...takes the kid 2 hours to completely trash while parents are cleaning and the parents are given on 4/5ths of an hours over the kid??? I think my 24.5 hours is more correct...the kid is trashing at 3.5 times the rate of the clean up...this is of course just my theory...the answer in the back...I bet they know more than I???

I did the problem in a very unorthodox form, but the answer's correct.

If f is a dirty house, then the toddler can reach f in two hours left alone; therefore, f/2 is the value per hour. If the parents can clenan up the house in seven hours, it is -f/7 per hour. If the number of hours is h, then the equation is h(f/2 + -f/7) = f. In order to check the answer, 2.8, or two and four fifths, is inserted; 2.8(f/2+-f/7) = f. divide by 2.8; f/2 + -f/7 = f/2.8. 7f/14 - 2f/14 = f/2.8 (this equation is the same as the last, but with the fractions adjusted for common denominators) is 5f/14 = f/2.8 Simplify the left side by dividing by five, and presto! f/2.8 = f/2.8. Therefore, the answer is 2.8 according to my checking procedure. As for solving the equation, someone else can do that.

h(f/2 + -f/7) = f. Divide by h; f/2 + -f/7 = f/h. Make it subtraction instead of adding a negative number for simplicity; f/2 - f/7 = f/h. Convert the two fractions on the left to fractions with a common denominator; 7f/14 - 2f/14 = f/h. Simplify by subtracting; 5f/14 = f/h. Simplify by reducing; f/2.8 = f/h. Multiply both sides by 1/f, then reduce: 2.8 = h.

I told you my method was a little unorthodox... It's a lot easier if you do it the less complex way above. Make f 1. It has no point being a variable.

The little tyke has a 3.5 hr advantage on the parents...if we start at perfectly clean.

IE...takes the tyke 2 hours to trash and 7 hours to clean...that gives the tyke a 3.5 hour advantage.

So it would take (I think 3.5 * 7 or 24.5 hours to completely trash the place)...we have other mathemiticans who can splain better then I and maybe come up with different answers????

let us let 0 on the y axis be the state of complete messiness, and 1 on the y axis be complete cleanliness. The x axis will represent time in hours. We know that it takes 7 hours for the parents to clean up completely (going from 0 to 1) so the slope of the parents' cleaning line will be 1/7 and the expression for the cleaning. the equation for cleaning of the apartment from any point of cleanliness will be y=(1/7)x+b. Similarly the child can take a clean appartment and mess it up in 2 hours. 1 to 0 is a change of -1 and over 2 hours makes the rate of -1/2 and the equation for dirtying is going to be y=(-1/2)x+b from any given cleanliness b.

Since we start with the place completely clean, b=1. We want a function that takes both rates of cleaning into account so, Y=((-1/2)+(1/7))X+1 Solve this for zero, but first simplify the slope into -7/14 + 2/14= -5/14, that is the slope of our combined function. So (-5/14)X+1=0 is what we must solve. (-5/14)X=-1 and X=-1(14/-5) so X=14/5= 2 and 4/5th hours.

With the parents and the child working "together", the total time would be the child working alone, PLUS the time to overcome the efforts of the parents working at the same time. The total time for the child to mess up the house has to be two hours PLUS the amount of time it takes to overcome the parents' efforts.

In one hour, the child working alone has done 1/2 the job. In one hour, the parents working alone have done 1/7 the job. But when they work together, messiness for one hour increases by 1/2 minus 1/7th, to account for the parents' efforts. This is 5/14, which is RELATIVE to the number of hours it would take if the child worked alone.

If messiness increases by 5/14 of the job, how long will it take to complete the entire job? That's the number which, when you multiply it by 5/14, will give unity, representing the whole job. In other words it's the reciprocal of 5/14, or 14/5, which is 2-4/5.

Total Time T = 1/(Child's Effort C - Parents' Effort P))

T = 1/(C-P)

This is an equation I am supposed to solve.


3X+1 6X+5
____ = ____

X-4 2X-7


The answer is

3Y+2
____

Y+3

The problems with just an = sign throw me. Do I multiply both sides by the least common factor or do I cross multiply or factor it out some way first?

(My brain is 99.9% verbally wired. I have a son who is my mirror image with math. I am amazed at his lack of vocabulary and such and he just cannot understand why everyone does not view the world through mathematical formulas. Of course he is not here to ask these questions and would think I was a retard if I did.)

The equation that you stated:

3X+1 6X+5
____ = ____

X-4 2X-7

has NO solution. That is, there is no value of X for which that
equality can be true.

If you cross multiply, you get

(3X + 1)(2X -7) = (6X + 5)(X-4)
multiplying out

6X^2 - 19X -7 = 6X^2 -19X -20

subtracting 6X^2 -19X from both sides

-7 = -20, which is impossible

in any case, a correct answer would not involve the variable Y, which did not appear in the original equation.

Copied that answer from the wrong section. The answer to this one is no such answer, so you are correct in the answer.