algebra

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you can paint a room in 8 hours. your friend and you can paint a room in 5 hours together. how long does it take your friend alone?

  • algebra -

    Your rate = room/8
    friends rate = room/x
    combined rate = room/8 + room/x
    = room(x+8)/(8x)

    then
    5 = room / [room(x+8)/(8x)]
    5 = 8x/(x+8)
    8x = 5x + 40
    3x = 40
    x = 40/3 = 13 1/3

    friend alone could do it in 13 hours and 20 minutes

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