An ordinary plane leaves an airport and flies due west at 180kph. Two hours later a jet leaves the same airport and flies due west at 900kph. How far from the airport will the jet overtake the ordinary plane?
distance traveled is the same
plane1:
d=180*t
Plane2
d=(900)(t-2)
set them equal
180t=900t-1800
solve for time t, then go solve for d in either equation.
To solve this problem, we can use the formula:
Distance = Speed × Time
Let's analyze the scenario step by step:
1. The ordinary plane leaves the airport and flies west at 180 km/h. We need to find out how far the plane will travel in the two-hour time period.
Distance_traveled_by_plane1 = Speed_plane1 × Time_plane1
Distance_traveled_by_plane1 = 180 km/h × 2 hours
Distance_traveled_by_plane1 = 360 km
So, after two hours, the ordinary plane will have traveled a distance of 360 kilometers from the airport.
2. The jet leaves the same airport two hours later and flies west at 900 km/h. To find out where the jet will overtake the ordinary plane, we need to determine how long it takes for the jet to catch up to the plane.
Since the jet is moving faster than the plane, it will eventually catch up to it. The time it takes for the jet to catch up to the ordinary plane can be determined by the equation:
Time_jet = Distance_traveled_by_plane1 / Relative Speed
Relative Speed = Speed_jet - Speed_plane1
Relative Speed = 900 km/h - 180 km/h
Relative Speed = 720 km/h
Time_jet = 360 km / 720 km/h
Time_jet = 0.5 hours
Therefore, it will take the jet 0.5 hours to catch up to the ordinary plane.
3. Now, to determine the distance from the airport where the jet will overtake the ordinary plane, we can use the formula:
Distance_from_airport = Speed_jet × Time_jet
Distance_from_airport = 900 km/h × 0.5 hours
Distance_from_airport = 450 kilometers
Therefore, the jet will overtake the ordinary plane at a distance of 450 kilometers from the airport.