A plane on a search mission flew east from an airport, turned, and flew west back to the airport. The plane cruised at 300km/h when flying east, and 400km/h when flying west. The plane was in the air for 7 hours. How far from the airport did the plane travel?

can you help me

i got 1200

To find the distance from the airport that the plane traveled, we need to determine the time it spent flying in each direction.

Let's assume the time spent flying east is "t" hours. Since the total time in the air is 7 hours, the time spent flying west would be 7 - t hours.

Now, we can calculate the distance traveled in each direction using the formula: Distance = Speed * Time.

When flying east, the distance covered would be 300 km/h * t hours = 300t km.
When flying west, the distance covered would be 400 km/h * (7 - t) hours = 400(7 - t) km.

Since the plane flew east from the airport and then turned around and flew west back to the airport, the total distance traveled is the sum of the distances in each direction. Therefore:

Total Distance = Distance East + Distance West
= 300t + 400(7 - t)
= 300t + 2800 - 400t
= 2800 - 100t

Now we can solve this equation to find the value of t.

2800 - 100t = 0
-100t = -2800
t = -2800 / -100
t = 28

The plane flew east for 28 hours. Therefore, the time spent flying west is 7 - 28 = -21 hours. However, since time cannot be negative in this context, it means the plane did not fly west. Instead, the entire journey of 7 hours was spent flying east.

Now, to find the total distance traveled:

Total Distance = Distance East
= 300t
= 300 * 28
= 8400 km

Therefore, the plane traveled a distance of 8400 km from the airport.