Two planes left an airport at noon. One flew East at a certain speed, and the other flew west at twice the eed of the first plane. The planes were 2700 miles apart in 3 hours. How fast was each plane flying? \[ 2700=r \cdot 3 \]

To determine the speeds of the two planes, let's break down the problem step by step. ### **Given:** 1. **Plane 1** flies **East** at a speed of **\( r \) miles per hour (mph)**. 2. **Plane 2** flies **West** at **twice** the speed of Plane 1, so its speed is **\( 2r \) mph**. 3. Both planes depart from the same airport at the same time (noon). 4. After **3 hours**, the distance between the two planes is **2700 miles**. ### **Objective:** Find the speed of each plane (\( r \) and \( 2r \)). ### **Solution:** 1. **Calculate the distance traveled by each plane in 3 hours:** - **Plane 1 (East-bound):** \[ \text{Distance}_1 = \text{Speed} \times \text{Time} = r \times 3 = 3r \text{ miles} \] - **Plane 2 (West-bound):** \[ \text{Distance}_2 = \text{Speed} \times \text{Time} = 2r \times 3 = 6r \text{ miles} \] 2. **Determine the total distance between the two planes after 3 hours:** Since the planes are flying in opposite directions (East and West), their distances add up. \[ \text{Total Distance} = \text{Distance}_1 + \text{Distance}_2 = 3r + 6r = 9r \text{ miles} \] 3. **Set up the equation using the given total distance:** \[ 9r = 2700 \] 4. **Solve for \( r \):** \[ r = \frac{2700}{9} = 300 \text{ mph} \] 5. **Determine the speed of each plane:** - **Plane 1 (East-bound):** \( r = 300 \) mph - **Plane 2 (West-bound):** \( 2r = 2 \times 300 = 600 \) mph ### **Conclusion:** - **Plane 1** was flying **East** at **300 mph**. - **Plane 2** was flying **West** at **600 mph**.