Question

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

Answer 1

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.