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Tyro
Asked: 2021-03-30T16:02:28+00:00 In:

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Working together,John and Mark painted a room in 10 hours.Last year,John paimted the room by himself.The year before, Mark painted it by himself but took 15 hours longer than John took.Assuming the rates did not change,how long did John and Mark take,when each painting alone?

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  2. acedstud

    Let the time it took John to paint the room by himself be x, then the time it took Mark to paint the room by himself is x+15.

    Painting together at the same rate, we have \dfrac{1}{x}+\dfrac{1}{x+15}=\dfrac{1}{10}

    Multiplying through the LCD, 10x(x+15), we have 10x(x+15)\cdot\dfrac{1}{x}+10x(x+15)\cdot\dfrac{1}{x+15}=10x(x+15)\cdot\dfrac{1}{10}.

    Thus, 10x+150+10x=x^2+15x

    \Rightarrow x^2-5x-150=0

    \Rightarrow (x-15)(x+10)=0

    \Rightarrow x-15=0 or x+10=0

    \Rightarrow x=15 or x=-10

    But x is a measure of time and must be positive, therefore x=15.

    Therefore, it took John 15 hours to paint the room by himself and it took Mark 15 + 15 = 30 hours to paint the room by himself.

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