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?
Let t be the time of the motion to east =>
300•t=400(7-t)
300t=400•7-400t
700t=400•7
t=4 hours
s=300•t=300•4=1200 km
thanks
To determine the distance the plane traveled, we can break down the problem into two parts: the distance covered while flying east, and the distance covered while flying west.
Let's denote the unknown distance as 'd' kilometers.
When flying east, the plane traveled at a speed of 300 km/h for a certain amount of time. Let's call this time 't' hours. So, the distance covered when flying east can be calculated using the formula: distance = speed × time. Therefore, the distance covered when flying east is 300t kilometers.
When flying west, the plane traveled at a speed of 400 km/h for the remaining time (7 - t) hours. The distance covered when flying west is 400(7 - t) kilometers.
Now, we can set up an equation to solve for the unknown distance 'd'. The total distance traveled is the sum of the distances covered when flying east and west:
d = 300t + 400(7 - t)
Now, we can simplify the equation:
d = 300t + 2800 - 400t
d = -100t + 2800
We want to find the value of 'd' when the plane was in the air for 7 hours, so we substitute t = 7 into the equation:
d = -100(7) + 2800
d = -700 + 2800
d = 2100
Therefore, the plane traveled 2100 kilometers from the airport.