Question

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?

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

100%

Answer 5

In 2 2/5 hours

Answer 6

25%?

Answer 7

25% per hour?

Answer 8

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?

Answer 9

thats correct

Answer 10

YEs so far

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

how to i break that down in simpler terms?

Answer 15

or fractions?

Answer 16

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?

Answer 17

yes

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

Sallys part + Johns part tells us how much is done in 1 hour

1/4 + 1/6 = ???

Answer 22

2 hours?

Answer 23

that would equal 2/10?

Answer 24

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?

Answer 25

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?

Answer 26

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 :)

Answer 27

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

Answer 28

common denominator would be 12?

Answer 29

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?

Answer 30

lol...

Answer 31

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

Answer 32

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

Answer 33

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 :)

Answer 34

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

Answer 35

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 :)

Answer 36

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

Answer 37

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

Answer 38

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

Answer 39

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

Answer 40

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

Answer 41

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

Answer 42

... I think its great :)

Answer 43

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

Answer 44

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

Answer 45

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

Answer 46

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.....

Answer 47

I think it should be 2 hours, 24 minutes.

Answer 48

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....

Answer 49

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\[T=2h+\frac{2}{5}h = 2h + \frac{2}{5}h.\frac{60\min}{h}=2h,24\min\]

Answer 50

I think Ezzie's over it...

Answer 51

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

Answer 52

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

Answer 53

is there a symbol for "else" ?

Answer 54

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

Answer 55

Not in particular.

Answer 56

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

Answer 57

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

Answer 58

guess it was just being stubborn when i tried yesterday

Answer 59

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

Answer 60

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?

Answer 61

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?

Answer 62

yep.....

Answer 63

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

Answer 64

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

Answer 65

That is 10 minutes.

Answer 66

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

Answer 67

maybe it 5/2 that.....

Answer 68

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

Answer 69

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

Answer 70

something like that ....

Answer 71

So you've found the error?

Answer 72

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

Answer 73

You had a lot of accounting going on.

Answer 74

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 ;)

Answer 75

Bah, at least it's over!

Answer 76

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