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?
key point:
at the "overtaking" they both will have gone the same distance in a time 2 hrs apart.
let the time taken by the jet be t hrs
then the time taken by the small plane be t+2 hrs
900t = 180(t+2)
900t = 180t + 360
720t = 360
t = 1/2
then 900t = 450
they will be together after 450 km
check:
jet went 900(1/2) = 450 km
small plane went 180(2 1/2)
= 180(5/2) = 450 km
Ok !
To determine the distance from the airport where the jet overtakes the ordinary plane, we need to consider their relative speeds.
Let x be the distance covered by the jet when it overtakes the ordinary plane.
At the time the jet overtakes the ordinary plane, the ordinary plane has been flying for 2 + (x/180) hours. This can be expressed as:
2 + (x/180) = (x/900)
Multiplying both sides of the equation by 900 gives:
1800 + 5x = x
Rearranging the equation, we have:
4x = 1800
Dividing by 4 gives:
x = 450
Therefore, the jet will overtake the ordinary plane 450 kilometers from the airport.
To determine the distance at which the jet overtakes the ordinary plane, we need to calculate the flight time of both planes and their distance covered during that time.
First, let's calculate the flight time of the ordinary plane. Since it flies at a constant speed of 180 kph, we can use the formula:
Flight time = Distance / Speed
Let's assume t1 as the flight time of the ordinary plane. Given that it flies for two hours, we have:
t1 = 2 hours
Next, let's calculate the flight time of the jet. Similarly, we can use the formula:
t2 = distance / speed
The speed of the jet is given as 900 kph, and since it departs two hours after the ordinary plane, the flight time can be represented as:
t2 = t1 - 2
Since both planes are flying due west, their distances traveled will be the speed multiplied by the flight time. Let d1 represent the distance covered by the ordinary plane, and d2 represent the distance covered by the jet.
d1 = 180 kph * t1
d2 = 900 kph * t2
To find the point where the jet overtakes the ordinary plane, we need to equate their distances traveled as they are moving at the same velocity:
d1 = d2
180 kph * t1 = 900 kph * t2
Now we can substitute the values of t1 and t2 from our earlier calculations:
180 kph * 2 = 900 kph * (2 - 2)
Simplifying the equation:
360 kph = 0 kph
Since the equation is not valid, it means that the jet will not overtake the ordinary plane. The two planes will never meet because the jet's speed is five times faster than the ordinary plane's speed.