document.write( "Question 496854: An airplane travels 5005km against the wind in 7 hours and 5635km with the wind in the same amount of time. 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 #336583 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"w\"$ = the wind speed
\n" ); document.write( "Let $\"p\"$ = the speed of the plane in still air
\n" ); document.write( "Against the wind, the plane's speed is $\"+p+-+w+\"$
\n" ); document.write( "With the wind, the plane's speed is $\"+p+%2B+w+\"$
\n" ); document.write( "given:
\n" ); document.write( "Equation against the wind:
\n" ); document.write( "(1) $\"+5005+=+%28+p+-+w+%29%2A7+\"$
\n" ); document.write( "With the wind:
\n" ); document.write( "(2) $\"+5635+=+%28+p+%2B+w+%29%2A7+\"$
\n" ); document.write( "This is 2 equations and 2 unknowns, so it's solvable
\n" ); document.write( "-----------------------
\n" ); document.write( "Add the equations
\n" ); document.write( "(1) $\"+7p+-+7w+=+5005+\"$
\n" ); document.write( "(2) $\"+7p+%2B+7w+=+5635+\"$
\n" ); document.write( " $\"+14p+=+10640+\"$
\n" ); document.write( " $\"+p+=+760+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+7p+-+7w+=+5005+\"$
\n" ); document.write( "(1) $\"+7%2A760+-+7w+=+5005+\"$
\n" ); document.write( "(1) $\"+5320+-+7w+=+5005+\"$
\n" ); document.write( "(1) $\"+7w+=+5320+-+5005+\"$
\n" ); document.write( "(1) $\"+7w+=+315+\"$
\n" ); document.write( "(1) $\"+w+=+45+\"$
\n" ); document.write( "The plane's speed in still air is 760 km/hr
\n" ); document.write( "The wind speed is 45 km/hr \n" ); document.write( "

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