Harry can rake leaves 8 hours faster than his little brother Jimmy. Together they can rake the leaves in 3 hours. Explain

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.