SOLUTION: Two planes start from the same airport and fly in opposite directions. The second plane starts 0.5 hours after the first plane, but it's speed is 80 km/hr faster. Find the speed of
Algebra ->
Customizable Word Problem Solvers
-> Travel
-> SOLUTION: Two planes start from the same airport and fly in opposite directions. The second plane starts 0.5 hours after the first plane, but it's speed is 80 km/hr faster. Find the speed of
Log On
Question 495658: Two planes start from the same airport and fly in opposite directions. The second plane starts 0.5 hours after the first plane, but it's speed is 80 km/hr faster. Find the speed of each plane if after 2 hours the planes are 3200 km apart.
I have tried setting up two seperate equations using the distance formula. The equations looked like this: 1600=2x, 1600=1.5(x+80). I am not sure what I am doing wrong. Answer by Edwin McCravy(20064) (Show Source):
You can put this solution on YOUR website! Two planes start from the same airport and fly in opposite directions. The second plane starts 0.5 hours after the first plane, but it's speed is 80 km/hr faster. Find the speed of each plane if after 2 hours the planes are 3200 km apart.
Is that 2 hours after the first plane left, or 2 hours after the second
plane left? You didn't tell us, and "after 2 hours" doesn't tell us,
So I'll have to do it both ways, and you'll have to ask your teacher
whether the 2 hours was after the first plane left or 2 hours after the
second plane left.
If it was 2 hours after the first plane left then the first plane
flew for 2 hours and the second plane flew for 1.5 hours.
If it was 2 hours after the second plane left then the first plane
flew for 2.5 hours and the second plane flew for 2 hours.
1. Assuming it was 2 hours after the first plane left.
Make this chart:
Distance Rate Time
First plane to leave
Plane that left later
Fill in those two times:
Distance Rate Time
First plane to leave 2
Plane that left later 1.5
Let x = the rate of the first plane to leave, and since the
second plane to leave was flying 80 km/hr faster, its rate
is x+ 80. So we fill those in:
Distance Rate Time
First plane to leave x 2
Plane that left later x+80 1.5
Now we fill in the Distances using Distance = Rate × Time
Distance Rate Time
First plane to leave 2x x 2
Plane that left later 1.5(x+80) x+80 1.5
The sum of the distances must equal 3200 km
2x + 1.5(x+80) = 3200
2x + 1.5x + 120 = 3200
3.5x + 120 = 3200
3.5x = 3080
x =
x = 880 km/hr
If the 2 hours is after the second plane left then
The first plane to leave traveled 880 kn/hr and the
second one to leave traveled 80 km/hr faster or 960 km/hr
----------------------------------------------
2. Assuming it was 2 hours after the second plane left, the
times are different
Distance Rate Time
First plane to leave 2.5x x 2.5
Plane that left later 2(x+80) x+80 2
The sum of the distances must equal 3200 km
2.5x + 2(x+80) = 3200
2.5x + 2x + 160 = 3200
4.5x + 160 = 3200
4.5x = 3040
x =
x =
x = 675.6 approximately
The first plane to leave traveled approximately 675.6 kn/hr and the
second one to leave traveled 80 km/hr faster or 755.6 km/hr approximately.
-------------------
The first way came out an exact answer. This one came out a fraction.
But either is feasible. Take your pick or ask your teacher which one
is the right one.
Edwin
