document.write( "Question 178714: Please help.
\n" ); document.write( "Debbie traveled by boat 5 miles upstream to fish in her favorite spot. Because of the 4-mph current, it took her 20 minutes longer to get there than to return. How fast will her boat go in still water?
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Algebra.Com's Answer #133680 by josmiceli(19441)\"\" \"About 
You can put this solution on YOUR website!
Let the speed of her boat in still water = \"s\"
\n" ); document.write( "Let the speed of the current = \"c\"
\n" ); document.write( "Against the current:
\n" ); document.write( "\"d%5B1%5D+=+r%5B1%5D%2At%5B1%5D\"
\n" ); document.write( "\"r%5B1%5D+=+s+-+c\"
\n" ); document.write( "\"d%5B1%5D+=+%28s+-+c%29%2At%5B1%5D\"
\n" ); document.write( "with the current:
\n" ); document.write( "\"d%5B2%5D+=+r%5B2%5D%2At%5B2%5D\"
\n" ); document.write( "\"r%5B2%5D+=+s+-+c\"
\n" ); document.write( "\"d%5B2%5D+=+%28s+%2B+c%29%2At%5B2%5D\"
\n" ); document.write( "-------------------------
\n" ); document.write( "given:
\n" ); document.write( "\"d%5B1%5D+=+5\" mi
\n" ); document.write( "\"d%5B2%5D+=+5\" mi
\n" ); document.write( "\"c+=+4\" mi/hr
\n" ); document.write( "\"t%5B1%5D+=+t%5B2%5D+%2B+20%2F60\" hr (20 min is 20/60 of an hour)
\n" ); document.write( "--------------------------
\n" ); document.write( "Now I can write:
\n" ); document.write( "(1) \"5+=+%28s+-+4%29%2A%28t%5B2%5D+%2B+1%2F3%29\"
\n" ); document.write( "(2) \"5+=+%28s+%2B+4%29%2At%5B2%5D\"
\n" ); document.write( "I have 2 equations and 2 unknowns, so it should be solvable
\n" ); document.write( "Since both (1) and (2) = \"5\", I'll set the right sides
\n" ); document.write( "equal to eachother
\n" ); document.write( "\"%28s+-+4%29%2A%28t%5B2%5D+%2B+1%2F3%29+=+%28s+%2B+4%29%2At%5B2%5D\"
\n" ); document.write( "Divide both sides by \"t%5B2%5D\"
\n" ); document.write( "\"%28s+-+4%29%2A%281+%2B+%281%2F3%29%2Ft%5B2%5D%29+=+s+%2B+4\"
\n" ); document.write( "\"s+-+4+%2B+%28s%2F3%29%2Ft%5B2%5D+-+%284%2F3%29%2Ft%5B2%5D+=+s+%2B+4\"
\n" ); document.write( "\"%28s%2F3+-+4%2F3%29%2Ft%5B2%5D+=+8\"
\n" ); document.write( "\"s%2F3+-+4%2F3+=+8t%5B2%5D\"
\n" ); document.write( "\"s+-+4+=+24t%5B2%5D\"
\n" ); document.write( "\"t%5B2%5D+=+%28s+-+4%29%2F24\"
\n" ); document.write( "Substitute this value of \"t%5B2%5D\" into (2)
\n" ); document.write( "(2) \"5+=+%28s+%2B+4%29%2At%5B2%5D\"
\n" ); document.write( "(2) \"5+=+%28s+%2B+4%29%28s+-+4%29%2F24\"
\n" ); document.write( "\"s%5E2+-+16+=+120\"
\n" ); document.write( "\"s%5E2+=+136\"
\n" ); document.write( "\"s+=+11.66\"
\n" ); document.write( "Her boat will go 11.66 mi/hr in still water
\n" ); document.write( "check answer:
\n" ); document.write( "(2) \"5+=+%28s+%2B+4%29%2At%5B2%5D\"
\n" ); document.write( "(2) \"5+=+%2811.66+%2B+4%29%2At%5B2%5D\"
\n" ); document.write( "\"5+=+15.66t%5B2%5D\"
\n" ); document.write( "\"t%5B2%5D+=+5%2F15.66\"
\n" ); document.write( "\"t%5B2%5D+=+.319\"hrs
\n" ); document.write( "\"t%5B1%5D+=+t%5B2%5D+%2B+20%2F60\"
\n" ); document.write( "\"t%5B1%5D+=+.319+%2B+.333\"
\n" ); document.write( "\"t%5B1%5D+=+.653\"hrs
\n" ); document.write( "------------------------
\n" ); document.write( "(1) \"5+=+%28s+-+4%29%2A%28t%5B2%5D+%2B+1%2F3%29\"
\n" ); document.write( "\"5+=+%2811.66+-+4%29%2A.653\"
\n" ); document.write( "\"5+=+7.66%2A.653\"
\n" ); document.write( "\"5+=+4.998\" close enough
\n" ); document.write( "(2) \"5+=+%28s+%2B+4%29%2At%5B2%5D\"
\n" ); document.write( "\"5+=+15.66%2A.319\"
\n" ); document.write( "\"5+=+4.995\" close enough
\n" ); document.write( "And, also \"t%5B1%5D\" should be 20 min
\n" ); document.write( "longer than \"t%5B2%5D\"
\n" ); document.write( "\"t%5B1%5D+-+t%5B2%5D+=+.653+-+.319\"
\n" ); document.write( "\".653+-+.319+=+.334\"
\n" ); document.write( "\".334%2A60+=+20.04\"min close enough\r
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