together it takes juan and mark 6 hours to paint a room. if it takes mark 15 hours by himself how long does it take juan by himself
Let J = rate at which juan can paint a room
Let M = rate at which mark can paint a room
Together they paint a room at a rate of 1 room / 6 hours
So, J + M = 1/6
Mark paints a room at a rate of 1 room / 15 hours
J + 1/15 = 1/6
J = 1/6 - 1/15 = 5/30 - 2/30 = 3/30 = 1/10
Therefore, juan can paint a room by himself in 10 hours
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