Answer
$35\ mph$ and $40\ mph$
Work Step by Step
Step 1. Assume the average velocity for the first engine is $x\ mph$; then the average velocity for the second engine is $x+5\ mph$.
Step 2. The total time spent by both engines is given by $\frac{140}{x}+\frac{200}{x+5}=9$.
Step 3. Multiply $x(x+5)$ on both sides. We have $140x+700+200x=9x^2+45x$ or $9x^2-295x-700=0$
Step 4. Factor the above equation as $(x-35)(9x+20)=0$; discard the negative solution. We have $x=35\ mph$ and $x+5=40\ mph$.
