Three Muralists

A city commissions a mural from three painters: Rosa, Ines, and Dmitri. Working solo, Rosa would need $120$ minutes to paint the whole wall, and Ines would need $100$ minutes. Rosa and Ines start together. After $40$ minutes of joint work, Dmitri shows up and pitches in, and the wall is finished exactly $10$ minutes later. How many minutes would Dmitri need to paint the entire mural by himself?