document.write( "Question 1025411: Flying against the wind, an airplane travels 3800km in 5 hours. Flying with the wind, the same plane travels 3660km in 3 hours. What is the rate of the plane in still air and what is the rate of the wind? \n" ); document.write( "

Algebra.Com's Answer #853904 by n2(78) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Flying against the wind, an airplane travels 3800km in 5 hours.
\n" ); document.write( "Flying with the wind, the same plane travels 3660km in 3 hours.
\n" ); document.write( "What is the rate of the plane in still air and what is the rate of the wind?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let u be the rate of the plane at no wind (in kilometers per hour)\r\n" );
document.write( "and v be the rate of the wind (in the same units).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then the effective rate  of the plane with   the wind is u + v\r\n" );
document.write( "and  the effective rate of the plane against the wind is u - v.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From the problem, the effective rate of the plane against the wind is the distance of 3800 kilometers \r\n" );
document.write( "divided by the time of 5 hours  {{3800/5}}} = 760 km/h.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "                  The effective rate of the plane with the wind is the distance of 3660 kilometers \r\n" );
document.write( "divided by the time of 3 hours   = 1220 mph.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, we have two equations to find 'u' and 'v'\r\n" );
document.write( "\r\n" );
document.write( "    u + v = 1220,    (1)\r\n" );
document.write( "\r\n" );
document.write( "    u - v =  760.    (2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To solve, add equations (1) and (2).  The terms 'v' and '-v' will cancel each other, and you will get\r\n" );
document.write( "\r\n" );
document.write( "    2u = 1220 + 760 = 1980  --->   u = 1980/2 = 990.\r\n" );
document.write( "\r\n" );
document.write( "Now from equation (1)\r\n" );
document.write( "\r\n" );
document.write( "     v = 1220 - 990 = 280 - 220 = 230.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The rate of the plane in still air is 990 km/h.  The rate of the wind is 230 km/h.\r\n" );
document.write( "

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

\n" );