document.write( "Question 436704: A plane flies 1500 miles against the wind in 3 hours and 45 minutes. The return trip with the wind takes 3 hours. Assume that the wind speed stays constant. Find the speed of the wind and the speed of the airplane with no wind. \n" ); document.write( "

Algebra.Com's Answer #853281 by ikleyn(53422) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A plane flies 1500 miles against the wind in 3 hours and 45 minutes.
\n" ); document.write( "The return trip with the wind takes 3 hours.
\n" ); document.write( "Assume that the wind speed stays constant.
\n" ); document.write( "Find the speed of the wind and the speed of the airplane with no wind.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        @mananth solved the problem making tons of unnecessary calculations.\r
\n" ); document.write( "\n" ); document.write( "        Therefore, his solution can scary a reader and is a bad way to teach.\r
\n" ); document.write( "\n" ); document.write( "        I will show below a standard solution approach to make minimum calculations.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "The flight against the wind took 3 hours and 45 minutes = 3 hours =  hours.\r\n" );
document.write( "\r\n" );
document.write( "The effective rate was   =  = 100*4 = 400 miles per hour.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It gives you first equation \r\n" );
document.write( "\r\n" );
document.write( "    u - v = 400  mph  (1),\r\n" );
document.write( "\r\n" );
document.write( "since the effective rate against the wind is the difference of the airspeed u and the rate of the wind v.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The flight with the wind took 3 hours.\r\n" );
document.write( "\r\n" );
document.write( "The effective rate was   = 500 miles per hour.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It gives you second equation \r\n" );
document.write( "\r\n" );
document.write( "    u + v = 500  mph  (2),\r\n" );
document.write( "\r\n" );
document.write( "since the effective rate with the wind is the sum of the airspeed u and the rate of the wind v.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now you have a system of two equations for u and v.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To find u, add equations (1) and (2).  The terms with 'v' cancel each other, and you will get\r\n" );
document.write( "\r\n" );
document.write( "    2u = 400 + 500 = 900,  u = 900/2 = 450.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now from equation (2)  v = 500 - 450 = 50.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus the problem is solved, and the ANSWER is\r\n" );
document.write( "\r\n" );
document.write( "     airspeed is 450 mph  (the rate in still air, or relative the air), and\r\n" );
document.write( "\r\n" );
document.write( "     the rate of the wind is 50 mph.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved, making the minimum calculations - making only those calculations that are really needed.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-----------------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now, after seeing my solution, it should be clear to you that the answer is the nice round numbers,
\n" ); document.write( "while ugly numbers from @mananth are (1) incorrect and (2) are the consequences of his
\n" ); document.write( "\"approximate\" calculations that only harm the solution.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Actually, the input numbers in this problem are \"very nice\" and lead to the nice
\n" ); document.write( "answer, if to treat the problem properly.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The way as I treat the problem in my post is the EXPECTED way on how the problem SHOULD be treated.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );