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.
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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
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in 1/2 hour north plan has traveled 100 miles. when other plane passes the point.
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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
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CHECK
400^2+300^2=500^2
