With a tailwind, a helicopter traveled 600 miles in 3 hrs. Flying against the wind on the return it took 4hrs to travel 1000 miles. Find the rate of the tail wind and the rate of the head wind.

When flying against the wind, the chopper is actually flying its rate MINUS the winds rate.

When flying with the wind, it is actually flying its rate PLUS the winds rate.

Let r_{H}=\text{helicopters rate}, \;\ r_{W}=\text{winds rate}

Since d=rt, then d/t=r

\frac{600}{3}=r_{H}+r_{W}\Rightarrow 200=r_{H}+R_{W}

\frac{1000}{4}=r_{H}-r_{W}\Rightarrow 250=r_{H}-r_{W}

You have two equations with two unknowns. Solve for r_{H} \;\ and \;\ r_{W}