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30 September, 15:48

Five divided by the difference of a number and 8 equals the quotient of 10 and the sum of a number and 7. Find the number.

If Jon can paint the fence in 3 hours and Karen can paint it in 5 hours, find how long takes them to paint it together.

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  1. 30 September, 17:07
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    Step-by-step explanation:

    Let the number be x

    Five divided by the difference of the number and 8 means

    5 / (x-8) and this is

    equals the quotient of 10 and the sum of a number and 7. This means

    10 / (7+x)

    Therefore,

    5 / (x-8) = 10 / (7+x)

    Cross multiplying,

    5 (7+x) = 10 (x-8)

    35 + 5x = 10x - 80

    5x - 10x = - 80 - 35

    -5x = - 115

    x = - 115/5 = 23

    2)

    If Jon can paint the fence in 3 hours

    This means Jon can paint the fence in 1/3 per hour

    If Karen can paint it in 5 hours

    This means Karen can paint the fence in 1/5 hours

    Their combined rate is additive since they work simultaneously. Jon doesn't stop for Karen to work and Karen doesn't stop for Jon to work.

    Their combined rate is

    1/3 + 1/5 = 8/15

    Let's assume the combined time is t hours.

    The combined time per hour is 1/t per hour. Therefore 1/t = 8/15

    t = 15/8 = 1.875 hours
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