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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?

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  1. amistre64
    • 5 years ago
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    this is an average question on any standardized test....

  2. amistre64
    • 5 years ago
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    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
    • 5 years ago
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    If it takes S 4 hours to complet the job, how much of the job is completed in 1 hour by S?

  4. anonymous
    • 5 years ago
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    100%

  5. anonymous
    • 5 years ago
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    In 2 2/5 hours

  6. anonymous
    • 5 years ago
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    25%?

  7. anonymous
    • 5 years ago
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    25% per hour?

  8. amistre64
    • 5 years ago
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    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
    • 5 years ago
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    thats correct

  10. anonymous
    • 5 years ago
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    YEs so far

  11. amistre64
    • 5 years ago
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    but try to put these in fractions, itll be easier to work with....at least it is for me :)

  12. amistre64
    • 5 years ago
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    John takes 6 hours to complete the same job, how much of the job is done by john in 1 hour?

  13. anonymous
    • 5 years ago
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    thats where im stuck how do i figuere that one out? It would bee 100 /6 ...

  14. anonymous
    • 5 years ago
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    how to i break that down in simpler terms?

  15. anonymous
    • 5 years ago
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    or fractions?

  16. amistre64
    • 5 years ago
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    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
    • 5 years ago
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    yes

  18. amistre64
    • 5 years ago
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    So Sally does 4 parts in 4 hours: 4/4 1 part for her is 1/4 right?

  19. anonymous
    • 5 years ago
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    yes... sorry i thoug he was doing 6 parts in 4 hours... that's why i was so confused...

  20. anonymous
    • 5 years ago
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    ok so sally does 1/4 of the work and and 1/6 for john got it!

  21. amistre64
    • 5 years ago
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    Sallys part + Johns part tells us how much is done in 1 hour 1/4 + 1/6 = ???

  22. anonymous
    • 5 years ago
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    2 hours?

  23. anonymous
    • 5 years ago
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    that would equal 2/10?

  24. amistre64
    • 5 years ago
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    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
    • 5 years ago
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    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
    • 5 years ago
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    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
    • 5 years ago
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    1/4 + 1/6 = how do we add fractions?

  28. anonymous
    • 5 years ago
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    common denominator would be 12?

  29. amistre64
    • 5 years ago
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    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
    • 5 years ago
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    lol...

  31. amistre64
    • 5 years ago
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    we need to change their tops to match ..... how do we do that? :)

  32. anonymous
    • 5 years ago
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    im not sure i cant remember... do we multiply top by 1//4 by 3 and 1/6 by 2?

  33. amistre64
    • 5 years ago
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    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
    • 5 years ago
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    3/12 + 2/12 = ...5/12.... tada!!

  35. amistre64
    • 5 years ago
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    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 :)

  36. radar
    • 5 years ago
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    How about 2 hours and 24 minutes I use product over sum 24/10=2.4 or 2 hours 24 minutes

  37. radar
    • 5 years ago
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    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

  38. radar
    • 5 years ago
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    Ezzie redo that last part and you will find the error.

  39. anonymous
    • 5 years ago
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    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

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

  41. anonymous
    • 5 years ago
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    \[= 1(3/12+2/12)\]

  42. anonymous
    • 5 years ago
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    ... I think its great :)

  43. anonymous
    • 5 years ago
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    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

  44. radar
    • 5 years ago
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    Yes by golly A takes time, it works out to 20, put A on the trim lol

  45. anonymous
    • 5 years ago
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    I think A needs to find another line of work :P

  46. amistre64
    • 5 years ago
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    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
    • 5 years ago
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    I think it should be 2 hours, 24 minutes.

  48. amistre64
    • 5 years ago
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    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
    • 5 years ago
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    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
    • 5 years ago
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    I think Ezzie's over it...

  51. anonymous
    • 5 years ago
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    What do those arrows represent? I don't think I've ever seen an equation with arrows.

  52. anonymous
    • 5 years ago
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    "Material Implication"...just means "If A then B"

  53. anonymous
    • 5 years ago
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    is there a symbol for "else" ?

  54. anonymous
    • 5 years ago
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    I only use them because the equation editor won't let you write things on a new line.

  55. anonymous
    • 5 years ago
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    Not in particular.

  56. anonymous
    • 5 years ago
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    I still havent figured out how to send an equation AND a sentence at once :P

  57. anonymous
    • 5 years ago
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    You type your sentence, call up 'Equation' below, type your equation, insert, and then keep typing :) ...

  58. anonymous
    • 5 years ago
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    guess it was just being stubborn when i tried yesterday

  59. anonymous
    • 5 years ago
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    Yeah, it's not very good. It freezes, stuff disappears, the matrix thing in it doesn't work...

  60. amistre64
    • 5 years ago
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    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
    • 5 years ago
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    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
    • 5 years ago
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    yep.....

  63. anonymous
    • 5 years ago
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    If you got to 5/12, then maybe it was just an arithmetic error.

  64. amistre64
    • 5 years ago
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    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
    • 5 years ago
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    That is 10 minutes.

  66. amistre64
    • 5 years ago
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    lol..... thats what I thought :) but it ainnt right

  67. amistre64
    • 5 years ago
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    maybe it 5/2 that.....

  68. amistre64
    • 5 years ago
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    there is 2 out of 5 parts left..... 60/5 = 12 times 2 = 24....found it :)

  69. anonymous
    • 5 years ago
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    It says this was going on 23 hours ago...is that right?

  70. amistre64
    • 5 years ago
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    something like that ....

  71. anonymous
    • 5 years ago
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    So you've found the error?

  72. amistre64
    • 5 years ago
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    yeah...it was my own stupidity as usual :)

  73. anonymous
    • 5 years ago
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    You had a lot of accounting going on.

  74. amistre64
    • 5 years ago
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    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
    • 5 years ago
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    Bah, at least it's over!

  76. anonymous
    • 5 years ago
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    Anyways, I'm out...happy mathing ;)

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