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If John can mow a the lawn in 4 hours and John and George together can mow it in 2 1/2 hours. Then how long does it take George to mow it by himself?

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  • Steven
    Lv 7
    9 years ago
    Favorite Answer

    if a does it in a certain time

    and b does it in a certain time

    1/a+1/b=1/c

    [still waiting for someone to tell me why it works]

    John =4

    total =2 1/2=5/2

    1/J+1/G=1/(5/2)

    1/4+1/G=2/5

    1/G=2/5-1/4

    1/G=8/20-5/20

    1/G=3/20

    G=20/3

    George takes 6 2/3 hours to mow the lawn himself

  • 9 years ago

    (time together / time alone1) + (time together / time alone2) = 1

    (5/2 / 4) + (5/2 / x) = 1

    5/(2x) = 1 - 5/8 = 3/8

    2x = 5 / (3/8) = 5(8/3) = 40/3

    x = 20/3

    It takes George 6 hours and 40 minutes to mow the lawn by himself.

  • Anonymous
    9 years ago

    Well I'd like to say 4 hours but it didn't half when old George came along so it might take longer , cause technically half the lawn takes John 2 hours , sounds like George is slow so must have taken him the two hours to do his half, by then johns done then starts helping him , so I'm gonna go with 5 hours 15 mins

  • 9 years ago

    You've got to subtract the rates. John is 1/4=0.25 lawns per hour, Together they do 1/2.5 0.4 lawns per hour.

    So George alone does 0.4 - 0.25 = 0.15 lawns per hour. This will take take 1/0.15 = 6 2/3 hours or 6 hours and 40 minutes.

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  • naveed
    Lv 4
    9 years ago

    formula is

    1/combined time=1/john time+1/mow time

    1/2.5=1/4+1/x

    1/2.5-1/4=1/x

    0.4-.25=1/x

    0.15=1/x

    or

    x=1/0.15

    x=6.67 hours

    so mow alone will take 6.67 hours to complete the job. hope it helps take care

  • 9 years ago

    1 and 1/4.

  • TC
    Lv 7
    9 years ago

    x + y = 1

    4x + y = 5/2

    y = - x + 1

    4x - x + 1 = 5/2

    3x = 5/2 - 2/2

    3x = 3/2

    x = 3/6 = 1/2 hour

    x + y = 1

    1/2 + y = 1

    y = 1/2

    1/2 hour

  • Mike G
    Lv 7
    9 years ago

    2.5*1/4 + 2.5G = 1

    2.5 + 10G = 4

    10G = 1.5

    G = 0.15 lawns/hour

    G takes 1/0.15 = 6.67 hours

  • 9 years ago

    4 hrs, why should it take any longer than John?

    No math involved at all in this question.

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