SOLUTION: In class we are doing systems of equations and solving by using substitution and elimination, but this is an apply it question. I am not sure how to set up my 2 equations for the

Question 931052: In class we are doing systems of equations and solving by using substitution and elimination, but this is an apply it question. I am not sure how to set up my 2 equations for the problem below is there any way you can help me understand what to do?
One plane leaves NYC traveling to LA at 550 mph. At the same time another plane leaves LA for NYC going 650 mph. If the 2 cities are 3000 miles apart how far are the planes from LA when they cross paths?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
One plane leaves NYC traveling to LA at 550 mph. At the same time another plane leaves LA for NYC going 650 mph. If the 2 cities are 3000 miles apart how far are the planes from LA when they cross paths?
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dist + dist = 3000
A + B = 3000
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time - time = 0
A/550 - B/650 = 0
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Modify for elimination::
650A - 550B = 0
Divide thru by 50 to get::
13A - 11B = 0
13A + 13B = 13*3000
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Subtract and solve for "B":
24B = 13*3000
B = 1625 miles (distance traveled at 650 mph
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Solve for "A"::
A + B = 3000
A = 3000-1625 = 1375 miles (distance traveled at 550 mph)
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Ans: 1375 miles from LA
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Cheers,
Stan H.
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