- anonymous

If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?
Is this an average question how would i solve this?

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- amistre64

this is an average question on any standardized test....

- amistre64

the "key" is to find out how much work is done by each person in one hour....or given time period.... just so happens to be an hour here

- amistre64

If it takes S 4 hours to complet the job, how much of the job is completed in 1 hour by S?

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## More answers

- anonymous

100%

- anonymous

In 2 2/5 hours

- anonymous

25%?

- anonymous

25% per hour?

- amistre64

100% is done in 4 hours...... so in 1 hour what % of the work is done by one of the people?
If it takes Sally 4 hours by herself to do the job, then we know that in 1 hour she will have done 1/4 of the job...does that make sense?

- amistre64

thats correct

- anonymous

YEs so far

- amistre64

but try to put these in fractions, itll be easier to work with....at least it is for me :)

- amistre64

John takes 6 hours to complete the same job, how much of the job is done by john in 1 hour?

- anonymous

thats where im stuck how do i figuere that one out? It would bee 100 /6 ...

- anonymous

how to i break that down in simpler terms?

- anonymous

or fractions?

- amistre64

think of it this way.... for john.
John does 6 parts in 6 hours....right? that would be the whole job. what is 1 part of the job...whichis the amount of work done in 1 hour...
1 part of 6/6 is 1/6 right?

- anonymous

yes

- amistre64

So Sally does 4 parts in 4 hours: 4/4 1 part for her is 1/4 right?

- anonymous

yes... sorry i thoug he was doing 6 parts in 4 hours... that's why i was so confused...

- anonymous

ok so sally does 1/4 of the work and and 1/6 for john got it!

- amistre64

Sallys part + Johns part tells us how much is done in 1 hour
1/4 + 1/6 = ???

- anonymous

2 hours?

- anonymous

that would equal 2/10?

- amistre64

good job, so in one hour, if they work together they complete:
2 parts out of 10: 2/10 which can be reduced to 1/5 also right?

- anonymous

but the multiple choice questions are
A. 2 hours and 24 minutes
B. 3 hours and 12 minutes
C. 3 hours and 44 minutes
Would it be the first one?

- amistre64

hold on.... I didnt check your answer to see if it was correct...
Do you remember how to "add" fraction? they need a common denominator right?
you can just add 1+1 and 4+6..... that aint gonna workout :)

- amistre64

1/4 + 1/6 = how do we add fractions?

- anonymous

common denominator would be 12?

- amistre64

12 is a common denominator that they can share, lets use it...
how does this 12 help us out? what do we do to our fractions to get them wear the same pants?

- anonymous

lol...

- amistre64

we need to change their tops to match ..... how do we do that? :)

- anonymous

im not sure i cant remember... do we multiply top by 1//4 by 3 and 1/6 by 2?

- amistre64

thats right...
1/4 says...I like these 12's and I have this cute top to wear with it...ill wear my "3" to go with this 12.
1/6 comes along and goes... I like this 12.... I have a top to match it as well, Im gonna wear my 2 to match it...
1/4 struts out in her new 3/12 outfit..... 1/6 struts out in her new 2/12 outfit and they meet up :)

- amistre64

3/12 + 2/12 = ...5/12.... tada!!

- amistre64

so, we now know how much of the job is completed in 1 hour.... 5/12
how many hours do they gotta work to get 12/12 done?
1 hour = 5/12
2 hours = 10/12
how much is left? 2/12 which can be done in less than an hour.. 1/6 of an hour to be exact.
60 minutes is one hour, lets divide that by 6 and we get 10 minutes...
2 hours and 10 minutes to finish the job when they work as a team :)

- radar

How about 2 hours and 24 minutes I use product over sum 24/10=2.4 or 2 hours 24 minutes

- radar

There was a error in the calculation of total hrs. 12/12 divided by 5/12 does not equal 2 1/6 but actually comes out to be 2 2/5

- radar

Ezzie redo that last part and you will find the error.

- anonymous

I don't see the word reciprocal in here anywhere :P
1/4 + 1/6 = 5/12
the reciprocal is 12/5 which equals 2 2/5 or 2.4 which is 2 hours and 24 minutes
because (60/5)*2=24 or 60*.4=24

- radar

\[T=1/(1/4 +1/6)=1(6/24 + 4/24)=1/(10/24)=24/10=2.4 hrs.\] Hows that for some reciprocals?!!

- anonymous

\[= 1(3/12+2/12)\]

- anonymous

... I think its great :)

- anonymous

So I guess that would mean,
If AB&C can do it in 2 days
B can do it in 4
C can do it in 5
A could do it in...
A= 1/(1/2-(1/4+1/5))
A= 20

- radar

Yes by golly A takes time, it works out to 20, put A on the trim lol

- anonymous

I think A needs to find another line of work :P

- amistre64

Ive been thinking whether my answer was wrong, or the options....
1/4 + 1/6 is right, I know that :)
(6+4)/24 = 10/24, thats good...
10/24 + 10/24 + 4/24 = 24/24...so 2 hours and 4/24
4/24 = 2/12 = 1/6
60 minutes equals an hour, I cut that into 6 equal portions and get 10 minutes each. I still get 2 hours and 10 minutes...
Cant see anything wrong with the math.....

- anonymous

I think it should be 2 hours, 24 minutes.

- amistre64

your probably right, but I cant seem to get to that answer... and this is the way ive always worked these and gotten them right....

- anonymous

Well, if T is the total time they will spend painting the house, then you have,\[R_sT+R_jT=W\]where\[R_s=\frac{W}{4h}, R_j=\frac{W}{6h}\]where the R_i are the rates at which Sally and John paint the (W)hole house. That means,\[W=\frac{W}{4h}T+\frac{W}{6h}T \rightarrow \frac{1}{T}=\frac{1}{4h}+\frac{1}{6h} \rightarrow T= \frac{12}{5}\]So\[T=2h+\frac{2}{5}h = 2h + \frac{2}{5}h.\frac{60\min}{h}=2h,24\min\]

- anonymous

I think Ezzie's over it...

- anonymous

What do those arrows represent? I don't think I've ever seen an equation with arrows.

- anonymous

"Material Implication"...just means "If A then B"

- anonymous

is there a symbol for "else" ?

- anonymous

I only use them because the equation editor won't let you write things on a new line.

- anonymous

Not in particular.

- anonymous

I still havent figured out how to send an equation AND a sentence at once :P

- anonymous

You type your sentence, call up 'Equation' below, type your equation, insert, and then keep typing :) ...

- anonymous

guess it was just being stubborn when i tried yesterday

- anonymous

Yeah, it's not very good. It freezes, stuff disappears, the matrix thing in it doesn't work...

- amistre64

I stil dont see where I went wrong with my logic...... we both get to 5/12 of the work being done in one hour.. or is that in error?

- anonymous

I didn't read through it...just went from the question. It sounds like you approached it from a basis point of view, as in, taking a basis of one hour. Did you?

- amistre64

yep.....

- anonymous

If you got to 5/12, then maybe it was just an arithmetic error.

- amistre64

my problem appears to be when I get to the third hour... there is 2/12 of the job left...... somehow I am equating that to 10 minutes

- anonymous

That is 10 minutes.

- amistre64

lol..... thats what I thought :) but it ainnt right

- amistre64

maybe it 5/2 that.....

- amistre64

there is 2 out of 5 parts left..... 60/5 = 12 times 2 = 24....found it :)

- anonymous

It says this was going on 23 hours ago...is that right?

- amistre64

something like that ....

- anonymous

So you've found the error?

- amistre64

yeah...it was my own stupidity as usual :)

- anonymous

You had a lot of accounting going on.

- amistre64

i was thinking that 12 parts were being done in 1 hour....that was my error. 5 parts are doen in 1 hour which means 12 minutes for each part and 2 parts is 24 minutes.....see, own stupidity ;)

- anonymous

Bah, at least it's over!

- anonymous

Anyways, I'm out...happy mathing ;)

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