SOLUTION: Airplane A travels 2800 km at a certain speed. Plane B travels 2000 km at a speed 50 km/hr faster than Plane A in 3 hrs less time. Find the speed of each plane

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Question 350638: Airplane A travels 2800 km at a certain speed. Plane B travels 2000 km at a speed 50 km/hr faster than Plane A in 3 hrs less time. Find the speed of each plane
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rate*Time=Distance
R%2At=D
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For Plane A,
1.R%5Ba%5D%2At=2800
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For Plane B,
2.%28R%5Ba%5D%2B50%29%2A%28t-3%29=2200
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From eq. 1,
t=2800%2FR%5Ba%5D
Substitute into eq. 2,
%28R%5Ba%5D%2B50%29%2A%282800%2FR%5Ba%5D-3%29=2200
%28R%5Ba%5D%2B50%29%2A%282800-3R%5Ba%5D%29=2200%2AR%5Ba%5D
2800R%5Ba%5D-3R%5Ba%5D%5E2%2B140000-150R%5Ba%5D=2200R%5Ba%5D
3R%5Ba%5D%5E2-450R%5Ba%5D-140000=0
Use the quadratic formula,
R%5Ba%5D+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
R%5Ba%5D+=+%28450+%2B-+sqrt%28+%28-450%29%5E2-4%2A3%2A%28-140000%29+%29%29%2F%282%2A3%29+
R%5Ba%5D+=+%28450+%2B-+sqrt%28+202500%2B1680000+%29%29%2F%286%29+
R%5Ba%5D+=+%28450+%2B-+sqrt%28+1882500+%29%29%2F%286%29+
Use only the positive answer.
R%5Ba%5D+=+%28450+%2B+1372%29%29%2F%286%29+
highlight%28R%5Ba%5D=303.7%29kph
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R%5Bb%5D=303.7%2B50
highlight%28R%5Bb%5D=353.7%29kph