Answer
$0.5$ hour, $2.5$ hours.
Work Step by Step
1. Assume Hazel need $x$ hours to do the job, he can do $\frac{1}{x}$ of the job per hour.
2. His friend needs $x+2$ hours and can do $\frac{1}{x+2}$ of the job per hour.
3. Together they need 2.4 hours for the job meaning $\frac{1}{2.4}$ of the job per hour.
4. We have $\frac{1}{x}+\frac{1}{x+2}=\frac{1}{2.4} \Longrightarrow 2x+2=2.4(x^2+2x) \Longrightarrow 1.2x^2+1.4x-1=0 \Longrightarrow 6x^2+7x-5=0 \Longrightarrow (2x-1)(3x+5)=0 \Longrightarrow x=0.5\ hour$ (positive answer only).
5. Thus it takes $0.5$ hour for Hazel, $2.5$ hours for her friend to do the job alone.
