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?
They would have traveled the same distance, let that distance be x km
time for jet = x/900
time for plane = x/180
x/180 - x/900 = 2
solve for x
hint: multiply each term by 900 , the LCD
To find out how far the jet will overtake the ordinary plane, we need to determine the time it takes for the jet to catch up to the ordinary plane.
Let's assume that the jet overtakes the ordinary plane at time t.
Since the ordinary plane travels for two hours before the jet takes off, the distance it covers in those two hours can be calculated as:
Distance covered by the ordinary plane = Speed of the ordinary plane × Time = 180 kph × 2 hours
Now, let's find the time it takes for the jet to catch up to the ordinary plane. We'll use the formula: Distance = Speed × Time.
Distance covered by the jet = Speed of the jet × Time = 900 kph × t
Since both the ordinary plane and the jet are traveling at the same speed (due west), the distance covered by both is the same when the jet overtakes the ordinary plane. Therefore:
Distance covered by the jet = Distance covered by the ordinary plane
We can set up the equation:
900t = 180 × 2
Simplifying the equation:
900t = 360
Now, divide both sides of the equation by 900:
t = 360 / 900
t ≈ 0.4 hours
Now that we have the time it takes for the jet to catch up to the ordinary plane, we can find the distance from the airport where the jet overtakes the ordinary plane.
Distance covered by the jet = Speed of the jet × Time = 900 kph × 0.4 hours
Calculating this equation:
Distance covered by the jet ≈ 360 km
Therefore, the jet will overtake the ordinary plane approximately 360 km from the airport.