document.write( "Question 30900: I am having a hard time with word problems if you could help me I would appreciate it here it goes: a plane flying with the wind went 600 miles in 3 hours. The return trip,flying against the wind took 4 hours. Find the rate of the plane in calm air and the rate of the wind. \n" ); document.write( "

Algebra.Com's Answer #17654 by Paul(988) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let the speed of the plane be x
\n" ); document.write( "Let the speed of the wind be y
\n" ); document.write( "3(x+y)=600 --->3x+3y=600
\n" ); document.write( "Solve for y in the first equation:
\n" ); document.write( "3y=600-3x
\n" ); document.write( "y=200-x (subsitution)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "4(x-y)=600
\n" ); document.write( "4x-4y=600
\n" ); document.write( "Subsitute for y:
\n" ); document.write( "4x-4(200-x)=600
\n" ); document.write( "4x-800+4x=600
\n" ); document.write( "8x=1400
\n" ); document.write( "x=175\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "y=200-175
\n" ); document.write( "y=25.
\n" ); document.write( "

Hence, the speed of the plane is 175mph and the speed of the wind is 25mph.
\n" );
document.write( "Paul. \n" );
document.write( "

\n" );