## anonymous 5 years ago 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?

1. amistre64

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

2. 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

3. amistre64

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

4. anonymous

100%

5. anonymous

In 2 2/5 hours

6. anonymous

25%?

7. anonymous

25% per hour?

8. 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?

9. amistre64

thats correct

10. anonymous

YEs so far

11. amistre64

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

12. amistre64

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

13. anonymous

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

14. anonymous

how to i break that down in simpler terms?

15. anonymous

or fractions?

16. 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?

17. anonymous

yes

18. amistre64

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

19. anonymous

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

20. anonymous

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

21. amistre64

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

22. anonymous

2 hours?

23. anonymous

that would equal 2/10?

24. 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?

25. 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?

26. 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 :)

27. amistre64

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

28. anonymous

common denominator would be 12?

29. 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?

30. anonymous

lol...

31. amistre64

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

32. anonymous

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

33. 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 :)

34. amistre64

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

35. 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 :)

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

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

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

39. 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

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

41. anonymous

$= 1(3/12+2/12)$

42. anonymous

... I think its great :)

43. 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

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

45. anonymous

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

46. 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.....

47. anonymous

I think it should be 2 hours, 24 minutes.

48. 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....

49. 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$T=2h+\frac{2}{5}h = 2h + \frac{2}{5}h.\frac{60\min}{h}=2h,24\min$

50. anonymous

I think Ezzie's over it...

51. anonymous

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

52. anonymous

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

53. anonymous

is there a symbol for "else" ?

54. anonymous

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

55. anonymous

Not in particular.

56. anonymous

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

57. anonymous

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

58. anonymous

guess it was just being stubborn when i tried yesterday

59. anonymous

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

60. 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?

61. 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?

62. amistre64

yep.....

63. anonymous

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

64. 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

65. anonymous

That is 10 minutes.

66. amistre64

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

67. amistre64

maybe it 5/2 that.....

68. amistre64

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

69. anonymous

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

70. amistre64

something like that ....

71. anonymous

So you've found the error?

72. amistre64

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

73. anonymous

You had a lot of accounting going on.

74. 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 ;)

75. anonymous

Bah, at least it's over!

76. anonymous

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