document.write( "Question 89075: An airplane can fly downwind a distance of 600 miles in 2 hours. The return trip against the same wind takes 3 hours. Find the speed of the wind. \n" ); document.write( "
Algebra.Com's Answer #64753 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "An airplane can fly downwind a distance of 600 miles in 2 hours. The return\r\n" );
document.write( "trip against the same wind takes 3 hours. Find the speed of the wind.\r\n" );
document.write( "\r\n" );
document.write( "Let w = the speed of the wind\r\n" );
document.write( "Let a = what the speed of the airplane would be if there were no wind\r\n" );
document.write( "\r\n" );
document.write( "Then going, flying with the wind, the wind makes the plane go faster,\r\n" );
document.write( "so we add the speed of the wind to what the speed of the plane would be\r\n" );
document.write( "if there were no wind.  Therefore,\r\n" );
document.write( "\r\n" );
document.write( "The actual speed going with the wind = a + w\r\n" );
document.write( "\r\n" );
document.write( "Now we use DISTANCE GOING = SPEED GOING × TIME GOING\r\n" );
document.write( "                      600 =  (a + w)×2\r\n" );
document.write( "                      600 = 2(a + w)\r\n" );
document.write( "Divide both sides by 2\r\n" );
document.write( "                      300 = a + w\r\n" );
document.write( "\r\n" );
document.write( "Now returning, flying against the wind, the wind makes the plane go \r\n" );
document.write( "slower, so we subtract the speed of the wind from what the speed of the \r\n" );
document.write( "plane would be if there were no wind.  Therefore,\r\n" );
document.write( "\r\n" );
document.write( "The actual speed returning against the wind = a - w\r\n" );
document.write( "\r\n" );
document.write( "Now we use DISTANCE RETURNING = SPEED RETURNING × TIME RETURNING\r\n" );
document.write( "                      600 =  (a - w)×3\r\n" );
document.write( "                      600 = 3(a - w)\r\n" );
document.write( "Divide both sides by 3\r\n" );
document.write( "                      200 = a - w \r\n" );
document.write( "\r\n" );
document.write( "Now you have two equations in two unknowns:\r\n" );
document.write( "\r\n" );
document.write( "                      300 = a + w\r\n" );
document.write( "                      200 = a - w \r\n" );
document.write( "\r\n" );
document.write( "Or maybe you would want to write them with the unknowns on the left:\r\n" );
document.write( "\r\n" );
document.write( "                      a + w = 300\r\n" );
document.write( "                      a - w = 200\r\n" );
document.write( "\r\n" );
document.write( "Solve them and get a = 250 mph and w = 50 mph\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So the speed of the airplane if there were no wind = 250 mph\r\n" );
document.write( "and the answer to the problem is:\r\n" );
document.write( "\r\n" );
document.write( "The speed of the wind is 50 mph\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "
\n" );