just checking to see if i have this problem correct

Question

Sammy can cut wood twice as fast as Joe. When they both work together, it takes them 4 hrs. how long would it take them to do the job alone?

4/x +4/x+2 = x^2+2

4x+4x+8= x^2+2
8x+8= x^2+2

x^2-6x-8=0

(x-4)(x+2)
x=4 x=-2 since i can't use a -2 i have to put in a 4

x+2=4+2=6

Sammy =6 hours
6x2=12
Joe = 12 hours

Thanks