document.write( "Question 1000926: a plane traveled 580 miles to zambaouga and back. the trip there was with the wind. it took 5 hours. the trip back was against the wind. the trip back was 10 hours. find the speed of the plane in still air and the speed of the wind \n" ); document.write( "

Algebra.Com's Answer #618274 by josgarithmetic(39620) $\"\"$ $\"About$

You can put this solution on YOUR website!

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\n" ); document.write( "\n" ); document.write( "Assigned Variable Values
\n" ); document.write( " $\"system%28t=5%2Cb=10%2Cd=580%29\"$
\n" ); document.write( "Think of t as \"to, with wind\", and b as \"back, against wind\".\r
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document.write( "           rate        time       distance\r\n" );
document.write( "WITH       r+w          t         d\r\n" );
document.write( "AGNST      r-w          b         d          \r\n" );
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\n" ); document.write( "Make the system of equations.
\n" ); document.write( " $\"system%28%28r%2Bw%29t=d%2C%28r-w%29b=d%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"system%28rt%2Bwt=d%2Crb-wb=d%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"tw=d-tr\"$
\n" ); document.write( " $\"w=d%2Ft-tr%2Ft\"$
\n" ); document.write( " $\"w=d%2Ft-r\"$
\n" ); document.write( "substitute,
\n" ); document.write( " $\"rb-%28d%2Ft-r%29b=d\"$
\n" ); document.write( " $\"br-db%2Ft%2Bbr=d\"$
\n" ); document.write( " $\"2br-db%2Ft=d\"$
\n" ); document.write( " $\"2br=d%2Bdb%2Ft\"$
\n" ); document.write( " $\"r=%28d%2Bdb%2Ft%29%2F2b\"$
\n" ); document.write( " $\"r=%28dt%2Ft%2Bdb%2Ft%29%2F2b\"$
\n" ); document.write( " $\"r=%28dt%2Bdb%29%2F%282bt%29\"$ ----you could use this form;
\n" ); document.write( " $\"highlight%28r=d%2F%282b%29%2Bd%2F%282t%29%29\"$ ----------plane speed absence of any wind, purely in symbols.\r
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\n" ); document.write( "\n" ); document.write( "Now find wind speed.
\n" ); document.write( " $\"w=d%2Ft-r\"$
\n" ); document.write( " $\"w=d%2Ft-d%2F%282b%29-d%2F%282t%29\"$ , simplest denominator is 2bt;
\n" ); document.write( " $\"w=%28d%2Ft%29%282b%2F%282b%29%29-%28d%2F%282b%29%29%28t%2Ft%29-%28d%2F%282t%29%29%28b%2Fb%29\"$
\n" ); document.write( " $\"highlight%28w=%282bt-dt-db%29%2F%282bt%29%29\"$ ---------wind speed in purely symbolic form.\r
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\n" ); document.write( "\n" ); document.write( "Substitute the given and known values to evaluate r and w.\r
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\n" ); document.write( "\n" ); document.write( "You also have the answer to many other exercise questions which fit this same travel rates type, because it is solved in symbolic form; just the given values would be different but the same general description is often given. \n" ); document.write( "

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