Home Remodeling -- Math Problem?

Sanchez Remodeling has three painters: Sue, Esther, and Murphy. Working together they can paint a large room in 4 hours. Sue and Murphy can paint the same size room in 6 hours. Esther and Murphy can paint the same size room in 7 hours. How long would it take each of them to paint the room alone?

Public Comments

1. let S, E and M be their rates of painting S + E + M = 1/4 S + M = 1/6 E + M = 1/7 From the first two, we get E = 1/12 ie E takes 12 hours From hte last, M = 5/84 ie M takes 16.8 hours From the second S = 3/28 ie S takes 9.33 hours