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You can put this solution on YOUR website!
\n" ); document.write( "Tutor @ikleyn shows a perfectly good method for solving the problem, finding the average speed with the wind and the average speed against the wind; then using algebra to set up two equations involving the plane's speed and the wind speed and solving them.
\n" ); document.write( "If the method of solving the problem is not specified, and in particular if the speed of solving a problem is important (as in a competitive exam), then here is another way to get from the two average speeds without algebra, using logical analysis and just a bit of simple arithmetic.
\n" ); document.write( "Think of the speeds on a number line. The speed of the plane is some number; if you add the speed of the wind, you get to some higher number, and if you subtract the speed of the wind, you get to some lower number.
\n" ); document.write( "Since you went the same distance in each direction to get to those other numbers, the speed of the plane is halfway between those two numbers.
\n" ); document.write( "So in this problem we have the two average speeds, with and against the wind, as 195 and 165 mph. The speed of the plane is halfway between those two speeds: 180 mph. Then the speed of the wind is how far 165 and 195 are away from 180, which is 15.
\n" ); document.write( "Without all the words of explanation, here is the solution process:
\n" ); document.write( "(1) average speed with the wind: 390/2 = 195
\n" ); document.write( "(2) average speed against the wind: 330/2 = 165
\n" ); document.write( "(3) plane speed: (195+165)/2 = 180 [halfway between 195 and 165; or average of 195 and 165]
\n" ); document.write( "(4) wind speed: 195-180 = 15, or 180-165 = 15
\n" ); document.write( "The computations with this method are exactly the computations you do using algebra; you just save the time of writing down the system of equations and solving them. \n" ); document.write( "