SOLUTION: An airplane flying north at 200 mph passed over a point on the ground at 2:00 PM. Another airplane at the same altitude passed over the point at 2:30 PM, flying east at 400 mph.

Question 358385: An airplane flying north at 200 mph passed over a point on the ground at 2:00 PM. Another airplane at the same altitude passed over the point at 2:30 PM, flying east at 400 mph. At what time were the planes 500 miles apart?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
An airplane flying north at 200 mph passed over a point on the ground at 2:00 PM. Another airplane at the same altitude passed over the point at 2:30 PM, flying east at 400 mph. At what time were the planes 500 miles apart?
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North plane 200 mph 2.00pm
East plane 400 mph 2.30 pm
...
in 1/2 hour north plan has traveled 100 miles. when other plane passes the point.
...
they are flying at right angles to each other.
when the east bound plane travels 2x miles north bound plane has traveled x+100 miles. ( because speed is half & it has 1/2 hour lead)
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(2x)^(x+100)^2= 500^2
4x^2+x^2+200x+10000=250000
5x^2+200x-240000=0
5x^2+1200x-1000x-240000=0
5x(x+240)-1000(x+240)=0
(x+240)(5x-1000)=0
5(x+240)(x-200)=0
x=200 miles
2x=400 miles: speed = 400 mph
time = distance/speed
400/400 = 1 hour
....
CHECK
400^2+300^2=500^2
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