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

So,

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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