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24 October, 09:25

it can take 12 hours to fill a swimming pool using two pipes. if the larger pipe is used for 4hrs and the smailler pipe of 9 hr only half the pool can be filled. how long will take each pipe to fill the pool seperately

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  1. 24 October, 09:45
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    large pipe = 20 hours

    small pipe = 30 hours

    x = larger pipe

    y = smaller pipe

    12 hours to fill swimming pool with both pipes:

    12x + 12y = 100%

    4 hrs large pipe and 9 hrs small pipe fills half the pool:

    4x + 9y = 50

    4x = 50 - 9y

    substitute "4x" in first equation with "50 - 9y" to solve for y:

    12x + 12y = 100

    3 (4x) + 12y = 100

    3 (50 - 9y) + 12y = 100

    150 - 27y + 12y = 100

    150 - 15y = 100

    -15y = - 50

    y = 50/15 = 10/3 = 3 1/3

    every hour, the small pipe fills the pool 3 1/3%

    Now use the value for y to solve for x:

    12x + 12y = 100

    12x + 12 (10/3) = 100

    12x + 40 = 100

    12x = 60

    x = 5

    every hour, the large pipe fills the pool 5%

    if the large pipe were filling the pool by itself, t = time it takes to fill 100%:

    100% = t * 5

    20 = t

    It would take 20 hours for the larger pipe to fill the pool by itself

    for the smaller pipe:

    100% = t * 10/3

    300/10 = t

    30 = t

    it would take 30 hours for the smaller pipe to fill the pool by itself
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