World problem about the equations of quadratic form

Question

Working together, Ging and Jovaine can mow a lawn in 4 hours and 48 minutes. If each of them will work alone, Jovaine can mow the lawn 4 hours longer than Ging can. How long will it take Ging, working alone, to mow the lawn?

Answer 1

4 hours and 48 minutes = 4.8 hours

1/(G+4) + 1/G = 1/4.8

multiply by 4.8G(G+4)

4.8G + 4.8(G+4) = G(G+4)

9.6G + 19.2 = G^2 + 4G

G^2 - 5.6G -19.2 = 0

(G-2.8)^2 = 19.2 + 2.8^2

G-2.8 = sqr(19.2 + 7.84)

G = 2.8 + or - 5.2 = 8 hours or a negative solution to be ignored

1/12 + 1/8 = 2/24 + 3/24 = 5/24 = 1/24/5 = 1/4.8

Ging can mow the lawn in 8 hours working alone

Jovaine can mow the lawn in 4+8 = 12 hours working alone