We need two equations for this.
A) (H * J) / (H + J) = 3
Harry is 8 hours faster than Jimmy
B) H + 8 = J
Inserting equation B into A gives us:
A) (H * (H+8))/ (H + H +8) = 3
H^2 +8H / (2H +8) = 3
H^2 + 8H = 6H + 24
H^2 + 2H -24 = 0
H = 4
and so J = 12
Harry takes 4 hours and Jimmy takes 12 hours.
