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A certain plane flying with the wind travels 540 km in 2 hours.
\n" ); document.write( " Later, flying against the same wind, the plane travels 690 km in 3 hours.
\n" ); document.write( " Find the speed of the plane in still air, and the speed of the wind.
\n" ); document.write( ":
\n" ); document.write( "let s = plane speed in still air
\n" ); document.write( "let w = speed of the wind
\n" ); document.write( "then
\n" ); document.write( "(s+w) = effective speed with the wind
\n" ); document.write( "(s-w) = effective speed against
\n" ); document.write( ":
\n" ); document.write( "Write two distance equations: dist = time * speed
\n" ); document.write( "2(s + w) = 540; (with the wind)
\n" ); document.write( "3(s - w) = 690; (against the wind}
\n" ); document.write( ":
\n" ); document.write( "We can simplify both these equations, divide the 1st by 2 and the 2nd by 3:
\n" ); document.write( "s + w = 270
\n" ); document.write( "s - w = 230
\n" ); document.write( "--------------addition eliminates w, find s
\n" ); document.write( "2s = 500
\n" ); document.write( "s = 250 km/hr speed in still air
\n" ); document.write( ":
\n" ); document.write( "Find the speed of the wind:
\n" ); document.write( "250 + w = 270
\n" ); document.write( "w = 270 - 250
\n" ); document.write( "w = 20 km/hr speed of the wind
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "A boat takes 3 hours to go 24 km upstream.
\n" ); document.write( "It can go 36 km downstream in the same time.
\n" ); document.write( " Find the speed of the current and the speed of the boat.
\n" ); document.write( ":
\n" ); document.write( "Do this problem exactly the same way:
\n" ); document.write( "3(s - c) = 24
\n" ); document.write( "3(s + c) = 36
\n" ); document.write( ":
\n" ); document.write( "Let me know if you need help. \n" ); document.write( "