SOLUTION: Two planes leave simultaneously from the same airport, one flying due east and the other due south. The eastbound plane is flying 100 miles per hour faster than the southbound plan

Question 213913: Two planes leave simultaneously from the same airport, one flying due east and the other due south. The eastbound plane is flying 100 miles per hour faster than the southbound plane. After 4 hours the planes are 3080 miles apart. Find the speed of each plane. (Use 1 decimal place.)
Found 2 solutions by checkley77, ankor@dixie-net.com:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
4(X+100)^2+4X^2=3080^2
4(X^2+200X+10,000)+4X^2=9,486,400
4X^2+800X+40,000+4X^2=9,486,400
8X^2+800X+40,000-9,486,400=0
8X^2+800X-9,446,400=0
8(X^2+100X-1,180,800)=0

X=(-100+-SQRT[100^2-4*1*-1,180,800])/281
X=(-100+-SQRT[10,000+4,723,200])/2
X=(-100+-SQRT4,733,200)/2
X=(-100+-2,175.5918)/2
X=(-100+2,175.5918)/2
X=2,075.5918/2
X=1,037.8 ANS. FOR THE SLOWER PLANE.
1,037.8+100=1,137.8 ANS. FOR THE FASTER PLANE.
PROOF:
4(1,137.8)^2+4*1,037.8^2=3080^2
4*1,294,588.8+4*1,077,028.8=9,486,400
5,178,355.2+4,308,115.2=9,486,400
9,486,400~9,486,400

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Two planes leave simultaneously from the same airport, one flying due east and the other due south.
The eastbound plane is flying 100 miles per hour faster than the southbound plane.
After 4 hours the planes are 3080 miles apart.
Find the speed of each plane. (Use 1 decimal place.)
:
The distance between the planes is the hypotenuse of a right triangle
a^2 + b^2 = c^2
:
Let s = speed of the southbound plane
then
(s+100) = speed of the eastbound
:
Dist = speed * time
:
a = 4s; south distance
b = 4(s+100); east distance
c = 3080; distance between the planes after 4 hrs
:
(4s)^2 + (4(s+100))^2 = 3080^2
:
16s^2 + (4s+400)^2 = 9486400
:
16s^2 + (4s+400)^2 = 9486400
:
16s^2 + 16s^2 + 3200s + 160000 = 948640
;
16s^2 + 16s^2 + 3200s + 160000 - 9486400 = 0
;
32s^2 + 3200s - 9326400 = 0
:
Simplify divide by 32:
s^2 + 100s - 291450 = 0
:
Using the quadratic formula; a=1; b=100; c=291450
;
I got a positive solution of 492.2 mph the south bound plane
:
then 592.2 mph the east bound plane
;
:
Check solution on a calc; enter = 3080
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