Question 587628
Yes, you have it right.
1/x * 18 + (1/x+3) * 18 = 5 
18/x + 18/(x+3) = 5 
multiplying both sides by (x)(x+3):
18(x+3) + 18x = 5(x)(x+3)
18x+54 + 18x = 5(x^2+3x)
36x+54 = 5x^2+15x
54 = 5x^2-21x
0 = 5x^2-21x-54
0 = 5x^2-30x+9x-54
0 = (5x^2-30x) + (9x-54)
0 = 5x(x-6) + 9(x-6)
0 = (x-6)(5x+9)
x = {-9/5, 6}
throw out the negative solution (extraneous) leaving:
x = 6 hours