document.write( "Question 769071: For a portion of the Green River in Utah, the rate of the river's current is 4 mph. A tour guide can row 6 mi down this river and back in 2 h. Find the rowing rate of the guide in calm water.\r
\n" ); document.write( "\n" ); document.write( "I'm having a hard time recalling how o set up a problem like this. I have tried:
\n" ); document.write( "with current distance: 6mi
\n" ); document.write( "with current rate: x+4
\n" ); document.write( "with current time: 6/x+4\r
\n" ); document.write( "\n" ); document.write( "Against current distance: 6mi
\n" ); document.write( "against current rate: x-4
\n" ); document.write( "against current time: 6/x-4\r
\n" ); document.write( "\n" ); document.write( "I'm unsure of how to set this up exactly with all this data or if I am even on the right track. Thanks for any help.
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Algebra.Com's Answer #468654 by ramkikk66(644)\"\" \"About 
You can put this solution on YOUR website!

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document.write( "For a portion of the Green River in Utah, the rate of the river's current is 4 mph. A tour guide can row 6 mi down this river and back in 2 h. Find the rowing rate of the guide in calm water. 
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document.write( "I'm having a hard time recalling how o set up a problem like this. I have tried:
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document.write( "with current distance: 6mi
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document.write( "with current rate: x+4
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document.write( "with current time: 6/x+4 
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document.write( "Against current distance: 6mi
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document.write( "against current rate: x-4
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document.write( "against current time: 6/x-4 
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document.write( "Ans:
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document.write( "You have started on the right track. As you have calculated till now, if we
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document.write( "assume that x is the speed of the boat in still water.
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document.write( "Time for downstream = 6/(x+4)
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document.write( "Time for upstream = 6/(x-4)
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document.write( "It is given that the total time (up and down) is 2 hours. So we get the
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document.write( "equation
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document.write( "\"6%2F%28x%2B4%29+%2B+6%2F%28x-4%29+=+2\" Cross multiplying
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document.write( "\"6%2A%28x-4%29%2B6%2A%28x%2B4%29+=+2%2A%28x%2B4%29%2A%28x-4%29\" Expanding the terms,
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document.write( "\"6%2Ax+-+24+%2B+6%2Ax+%2B+24+=+2%2A%28x%5E2+-+16%29\" 
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document.write( "\"12%2Ax+=+2%2Ax%5E2+-+32\" Simplifying
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document.write( "\"x%5E2+-+6%2Ax+-+16+=+0\"
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document.write( "This is a standard quadratic equation that you can solve by factorizing.
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document.write( "You get
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document.write( "\"x%5E2+-+8%2Ax+%2B+2%2Ax+-+16+=+0\"
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document.write( "\"x%2A%28x+-+8%29+%2B+2%2A%28x+-+8%29+=+0\"
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document.write( "\"%28x+-+8%29%2A%28x+%2B+2%29+=+0\"
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document.write( "x = 8 or x = -2
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document.write( "Since x cannot be negative, the speed of the boat in calm water is 8 mph.\r
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document.write( "Check for correctness:
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document.write( "If speed in still water is 8 mph
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document.write( "Time for downstream = 6/(8+4) = 0.5 hours
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document.write( "Time for upstream = 6/(8-4) = 1.5 hours
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document.write( "Total time = 0.5 + 1.5 = 2 hours.
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document.write( "Correct!\r
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document.write( "Hope you got it :) \n" );
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