document.write( "Question 920302: With a head wind, Ethan's plane traveled 1000 miles in 4 hours. With the same wind as a tail wind, the return trip took 3 hours 20 minutes. Find the plane's air speed and the wind speed. \n" ); document.write( "

Algebra.Com's Answer #558296 by mananth(16946) $\"\"$ $\"About$

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plane speed =x mph
\n" ); document.write( "wind speed given speed =y mph
\n" ); document.write( "against wind speed given 4 hours
\n" ); document.write( "with wind speed given 3 1/ 3 hours
\n" ); document.write( "
\n" ); document.write( "Distance against 1000 miles distance with 1000 miles
\n" ); document.write( "t=d/r against wind speed given -
\n" ); document.write( "1000 / ( x - y )= 4
\n" ); document.write( "4 ( x - y ) = 3 1/ 3
\n" ); document.write( "4 x - 4 y = 1000 ....................1
\n" ); document.write( "
\n" ); document.write( "1000 / ( x + y )= 10/ 3
\n" ); document.write( "3 1/ 3 ( x + y ) = 1000
\n" ); document.write( "10x + 10y = 3000
\n" ); document.write( "x+y=300 ...............2
\n" ); document.write( "Multiply (2) by 4
\n" ); document.write( "
\n" ); document.write( "we get
\n" ); document.write( "4x -4 y = 1200
\n" ); document.write( "add to (1)
\n" ); document.write( "8x=2200
\n" ); document.write( "/8
\n" ); document.write( "x = 275 mph
\n" ); document.write( " plug x in the eqution to get y
\n" ); document.write( "x+y=300
\n" ); document.write( "275+y=300
\n" ); document.write( "y=300-275
\n" ); document.write( " y = 25.00
\n" ); document.write( "plane speed 275.00 mph
\n" ); document.write( "wind speed given speed 25.00 mph
\n" ); document.write( " \n" ); document.write( "

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