document.write( "Question 109396: a jet plane travelling at a constant speed goes 1200 mi with the wind , then turns around and travels for 1000 mi against the wind . If the speed of the wind is constant 50 mph , and the total flight took 4 hrs , find the speed of the plane. \n" ); document.write( "
Algebra.Com's Answer #79893 by ankor@dixie-net.com(22740)\"\" \"About 
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jet plane traveling at a constant speed goes 1200 mi with the wind , then turns around and travels for 1000 mi against the wind . If the speed of the wind is constant 50 mph , and the total flight took 4 hrs , find the speed of the plane.
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\n" ); document.write( "Let s = speed of the plane
\n" ); document.write( "then
\n" ); document.write( "(s+50) = speed with the wind
\n" ); document.write( "and
\n" ); document.write( "(s-50) = speed against the wind
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\n" ); document.write( "Write a time equation: Time = dist/speed
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\n" ); document.write( "Time with + time against = 4 hr
\n" ); document.write( "\"1200%2F%28%28s%2B50%29%29\" + \"1000%2F%28%28s-50%29%29\" = 4
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\n" ); document.write( "Multiply equation by (s+50)(s-50) to eliminate the denominators:
\n" ); document.write( "(s+50)(s-50)*\"1200%2F%28%28s%2B50%29%29\" + (s+50)(s-50)*\"1000%2F%28%28s-50%29%29\" = 4(s+50)(s-50)
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\n" ); document.write( "Cancel out the denominators and you have;
\n" ); document.write( "1200(s-50) + 1000(s+50) = 4(s^2 - 2500)
\n" ); document.write( ":
\n" ); document.write( "1200s - 60000 + 1000s + 50000 = 4s^2 - 10000
\n" ); document.write( ":
\n" ); document.write( "2200s - 10000 = 4s^2 - 10000
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\n" ); document.write( "Arrange as quadratic equation on the left:
\n" ); document.write( "4s^2 - 2200s - 10000 + 10000 = 0
\n" ); document.write( ":
\n" ); document.write( "4s^2 - 2200s = 0
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\n" ); document.write( "Factor this:
\n" ); document.write( "4s(s - 550) = 0
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\n" ); document.write( "Solution:
\n" ); document.write( "4s = 0
\n" ); document.write( "s = 0
\n" ); document.write( "and
\n" ); document.write( "s = +550 mph is our solution; (speed of the plane in still air)
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\n" ); document.write( "Check our solution, find the time total:
\n" ); document.write( "speed with the wind: 600 mph
\n" ); document.write( "speed against the wind: 500 mph
\n" ); document.write( "1200/600 + 1000/500
\n" ); document.write( " 2 + 2 = 4hrs
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