SOLUTION: A private airplane leaves an airport and flies due east at 192 km/hr. Two hours later, a jet leaves the same airport and flies due east at 960 km/hr. How long after the jet leaves

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Question 1200493: A private airplane leaves an airport and flies due east at 192 km/hr. Two hours later, a jet leaves the same airport and flies due east at 960 km/hr. How long after the jet leaves will it overtake the plane?
Found 2 solutions by math_tutor2020, Alan3354:
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

kph = kilometers per hour

Let's call the planes A and B.

Plane A travels east at 192 kph
Plane B travels east at 960 kph, taking off 2 hours later.

A = slower plane
B = faster plane

x = amount of time the faster plane is in the air.

The slower plane got a 2 hour head start, so x+2 represents the number of hours the slower plane is flying.

Plane A
distance = rate*time
distance = 192*(x+2)

Plane B
distance = rate*time
distance = 960*x

The faster plane passes the slower one when the two aircraft have traveled the same distance.
distanceA = distanceB
192*(x+2) = 960x
192x+384 = 960x
384 = 960x-192x
384 = 768x
x = 384/768
x = 0.5

This leads to x+2 = 0.5+2 = 2.5

Plane A is in the air for 2.5 hrs (aka 2.5*60 = 150 min, aka 2 hrs + 30 min)
Plane B is in the air for 0.5 hrs (aka 0.5*60 = 30 min)

Check:
plane A's distance = 192*2.5 = 480 km
plane B's distance = 960*0.5 = 480 km
Both have traveled the same distance, so the answer is confirmed.


Answer: 0.5 hours aka 30 minutes

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A private airplane leaves an airport and flies due east at 192 km/hr. Two hours later, a jet leaves the same airport and flies due east at 960 km/hr. How long after the jet leaves will it overtake the plane?
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1) Find the distance "d" the 1st plane is from the airport in 2 hours.
2) Find the difference in speed "r" of the 2 planes.
3) d = r*t ---> t = d/r