document.write( "Question 107933: One plane flew 390 km with the help of a tailwind in twice the time that another plane flew 180 km against the headwind. If each plane can fly 500 km/h in still air, find the rate of the tailwind. \n" ); document.write( "
Algebra.Com's Answer #78784 by ankor@dixie-net.com(22740)\"\" \"About 
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One plane flew 390 km with the help of a tailwind in twice the time that another plane flew 180 km against the headwind. If each plane can fly 500 km/h in still air, find the rate of the tailwind.
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\n" ); document.write( "Let x = rate of the wind:
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\n" ); document.write( "(500+x) = speed with the wind
\n" ); document.write( "(500-x) = speed against the wind
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\n" ); document.write( "Write a time equation: Time = Distance/speed
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\n" ); document.write( "With time = twice against time
\n" ); document.write( "\"390%2F%28%28500%2Bx%29%29\" = \"2%28180%2F%28%28500-x%29%29%29\"
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\n" ); document.write( "\"390%2F%28%28500%2Bx%29%29\" = \"360%2F%28%28500-x%29%29\"
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\n" ); document.write( "Cross multiply:
\n" ); document.write( "360(500+x) = 390(500-x)
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\n" ); document.write( "180000 + 360x = 195000 - 390x
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\n" ); document.write( "360x + 390x = 195000 - 180000
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\n" ); document.write( "750x = 15000
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\n" ); document.write( "x = 15000/750
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\n" ); document.write( "x = 20 mph is the speed of the wind
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\n" ); document.write( "Check solution by finding the time relationship
\n" ); document.write( "390/520 = .75
\n" ); document.write( "180/480 = .375; confirms our solution
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\n" ); document.write( "Did this make sense to you? Any questions? \n" ); document.write( "
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