document.write( "Question 106884This question is from textbook
\n" ); document.write( ": Plane A can travel 1500 miles in 1 hour less time than it takes plane B to travel 2500 miles. If the rate of plane B is 50 miles per hour greater than the rate of plane A. Find the times and rates of both planes. \n" ); document.write( "
Algebra.Com's Answer #77885 by ptaylor(2198)\"\" \"About 
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\n" ); document.write( "distance(d) equals rate(r) times time(t) or d=rt; r=d/t and t=d/r\r
\n" ); document.write( "\n" ); document.write( "Let r=rate of Plane A
\n" ); document.write( "Then r+50=rate of Plane B\r
\n" ); document.write( "\n" ); document.write( "Time for Plane B to travel 2500 mi=2500/(r+50)
\n" ); document.write( "Time for Plane A to travel 1500 mi=1500/r\r
\n" ); document.write( "\n" ); document.write( "Now we are told that Plane A takes 1 hour less time than it takes Plane B, so:\r
\n" ); document.write( "\n" ); document.write( "(1500/r)+1=2500/(r+50) multiply each term by r(r+50) and we get:\r
\n" ); document.write( "\n" ); document.write( "1500(r+50)+r(r+50)=2500r get rid of parens (distributive law)
\n" ); document.write( "1500r+75000+r^2+50r=2500r subtract 2500r from both sides\r
\n" ); document.write( "\n" ); document.write( "1500r-2500r+75000+r^2+50r=2500r-2500r collect like terms\r
\n" ); document.write( "\n" ); document.write( "r^2-950r+75000=0 quadratic in standard form\r
\n" ); document.write( "\n" ); document.write( "Solve using the quadratic formula:\r
\n" ); document.write( "\n" ); document.write( "\"r+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( "\"r+=+%28950+%2B-+sqrt%28+950%5E2-4%2A1%2A75000+%29%29%2F%282%2A1%29+\"
\n" ); document.write( "\"r+=+%28950+%2B-+sqrt%28+902500-300000+%29%29%2F%282%29+\"
\n" ); document.write( "\"r+=+%28950+%2B-+sqrt%28602500+%29%29%2F%282%29+\"
\n" ); document.write( "\"r+=+%28950+%2B-+776.21+%29%29%2F%282%29+\" So, looks like two solutions to me. Lets find out.\r
\n" ); document.write( "\n" ); document.write( "\"r+=+%28950%2B776.21+%29%29%2F%282%29+\"
\n" ); document.write( "\"r+=+%281726.21+%29%29%2F%282%29+\" \r
\n" ); document.write( "\n" ); document.write( "\"r+=+863.10+\" mph-----------------------rate of plane A
\n" ); document.write( "Time for Plane A=1500/r=1500/863.10=1.738 hrs
\n" ); document.write( "\"r%2B50=863.10%2B50=913.10\" mph---------------rate of Plane B
\n" ); document.write( "Time for Plane B=2500/913.10=2.738 hrs-------------------1 hr longer
\n" ); document.write( "and
\n" ); document.write( "\"x+=+%28950-776.21+%29%29%2F%282%29+\"
\n" ); document.write( "\"x+=+%28173.79+%29%29%2F%282%29+\"
\n" ); document.write( "\"x+=+86.895\" mph----------------------rate of Plane A
\n" ); document.write( "Time for Plane A=1500/86.895=17.262 hrs
\n" ); document.write( "\"r%2B50=86.895%2B50=136.895\" mph---------------rate of Plane B
\n" ); document.write( "Time for Plane B=2500/136.895=18.262 hrs-----------------------1 hr longer\r
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\n" ); document.write( "\n" ); document.write( "Hope this helps-----ptaylor\r
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