1. **State the problem:** Two planes are 3600 miles apart and fly toward each other. Their rates differ by 90 miles per hour. We need to find each plane's speed if they meet in 5 hours. 2. **Define variables:** Let the speed of the slower plane be $x$ miles per hour. Then the speed of the faster plane is $x+90$ miles per hour. 3. **Express the total distance covered:** Since they fly toward each other, their combined speed is $x + (x+90) = 2x + 90$ miles per hour. 4. **Distance-time relationship:** The planes meet after 5 hours, so the total distance covered by both is: $$ (2x + 90) \times 5 = 3600 $$ 5. **Solve the equation:** $$ 5(2x + 90) = 3600 $$ $$ 10x + 450 = 3600 $$ $$ 10x = 3600 - 450 $$ $$ 10x = 3150 $$ $$ x = \dfrac{3150}{10} = 315 $$ 6. **Find the speeds:** Slower plane speed: $315$ mph Faster plane speed: $315 + 90 = 405$ mph **Final answer:** The slower plane flies at 315 miles per hour and the faster plane flies at 405 miles per hour.