document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=19478>Question 19478</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this problem I have exhausted all of my resources to try and figure it out.\r<BR>\n" );
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document.write( "On a windy day Yoshiaki found that he could go 16mi downstream and then 4mi back upstream at top speed in a total of 48min.  What was the top speed of Yoshiaki's boat if the current was 15mph?<BR>\n" );
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document.write( "The answer in the back of the book is 25mph, but I can't seem to figure out how they came up with that answer.  We are working with quadratic equations.  Here is what I have tried:<BR>\n" );
document.write( "______________D_____R________T_______<BR>\n" );
document.write( "upstream:_____4mi___x-15___4/(x-15)<BR>\n" );
document.write( "downstream:___16mi__x+15___16/(x+15)<BR>\n" );
document.write( "_____________________________________<BR>\n" );
document.write( "4/(x-15) + 16/(x+15) = 48 \r<BR>\n" );
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document.write( "I cannot seem to come up with the answer 25, I must be doing something wrong in the form of the equation.  Please Help!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #9410 by </B><A HREF=/tutors/aboutme.mpl?userid=xcentaur><B>xcentaur(357)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=xcentaur><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=9410\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the speed of the boat be x mph<BR>\n" );
document.write( "let the speed of the current be y mph<BR>\n" );
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document.write( "Then while going downstream,<BR>\n" );
document.write( "distance downstream=16miles<BR>\n" );
document.write( "speed=(x+y) [since the current helps the boat]<BR>\n" );
document.write( "time taken=d/s=16/(x+y).......[1]<BR>\n" );
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document.write( "while going upstream,<BR>\n" );
document.write( "distance upstream=4 miles<BR>\n" );
document.write( "speed=(x-y) [since the current is in the opposite direction of the boat]<BR>\n" );
document.write( "time taken=d/s=4/(x-y).........[2]<BR>\n" );
document.write( "<P><BR>\n" );
document.write( "Now we have been told that the total time taken is 48 minutes<BR>\n" );
document.write( "48 minutes means : (48/60)hour=(4/5)hour<BR>\n" );
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document.write( "Add up both the times we got (equations 1 and 2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816%2F%28x%2By%29%29%2B%284%2F%28x-y%29%29=4%2F5 ALIGN=MIDDLE  ALT=\"%2816%2F%28x%2By%29%29%2B%284%2F%28x-y%29%29=4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816%28x-y%29%2B4%28x%2By%29%29%2F%28%28x%2By%29%28x-y%29%29=4%2F5 ALIGN=MIDDLE  ALT=\"%2816%28x-y%29%2B4%28x%2By%29%29%2F%28%28x%2By%29%28x-y%29%29=4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816x-16y%2B4x%2B4y%29%2F%28x%5E2-y%5E2%29=4%2F5 ALIGN=MIDDLE  ALT=\"%2816x-16y%2B4x%2B4y%29%2F%28x%5E2-y%5E2%29=4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820x-12y%29=4%2F5%28x%5E2-y%5E2%29 ALIGN=MIDDLE  ALT=\"%2820x-12y%29=4%2F5%28x%5E2-y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we have been told in the question that the speed of the current (y) is 15 mph<BR>\n" );
document.write( "So we get,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820x-12%2815%29%29=4%2F5%28x%5E2-%2815%29%5E2%29 ALIGN=MIDDLE  ALT=\"%2820x-12%2815%29%29=4%2F5%28x%5E2-%2815%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20x-180=4%2F5%28x%5E2-225%29 ALIGN=MIDDLE  ALT=\"20x-180=4%2F5%28x%5E2-225%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "opening the brackets<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20x-180=4%2F5x%5E2-4%2F5%28225%29 ALIGN=MIDDLE  ALT=\"20x-180=4%2F5x%5E2-4%2F5%28225%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20x-180=4%2F5x%5E2-4%2845%29 ALIGN=MIDDLE  ALT=\"20x-180=4%2F5x%5E2-4%2845%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20x-180=4%2F5x%5E2-180 ALIGN=MIDDLE  ALT=\"20x-180=4%2F5x%5E2-180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "now '-180' cancels off<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20x=4%2F5x%5E2 ALIGN=MIDDLE  ALT=\"20x=4%2F5x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100x=4x%5E2 ALIGN=MIDDLE  ALT=\"100x=4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x=x%5E2 ALIGN=MIDDLE  ALT=\"25x=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which can be written as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x=x%2Ax ALIGN=MIDDLE  ALT=\"25x=x%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cancelling out the x we get,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25=x ALIGN=MIDDLE  ALT=\"25=x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=25 ALIGN=MIDDLE  ALT=\"x=25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<P><BR>\n" );
document.write( "And so we get the top speed of the boat(x) = 25 mph<BR>\n" );
document.write( "<P><font color=blue><BR>\n" );
document.write( "Hope this helps,<BR>\n" );
document.write( "Prabhat</font> </SPAN>\n" );
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