document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=909392>Question 909392</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ship is anchored 9 miles from the nearest point of a straight beach. A man in the ship wishes to row to the shore and walk to a point on the beach 17 miles from the point directly opposite the ship. If he can row at the rate of 4 miles per hour and walk at the rate of 5 miles per hour, where ought he to land in order to reach his destination in 4 hour and 45 minutes? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #551914 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=551914\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A ship is anchored 9 miles from the nearest point of a straight beach.<BR>\n" );
document.write( " A man in the ship wishes to row to the shore and walk to a point on the beach 17 miles from the point directly opposite the ship.<BR>\n" );
document.write( " If he can row at the rate of 4 miles per hour and walk at the rate of 5 miles per hour, where ought he to land in order to reach his destination in 4 hour and 45 minutes?<BR>\n" );
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document.write( "A right triangle is formed by the ship, point on the shore directly opposite the ship, and a point on the landing point on the shore<BR>\n" );
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document.write( "Let x = dist between the opposite point and the landing point<BR>\n" );
document.write( "The rowing path will be the hypotenuse of the triangle<BR>\n" );
document.write( "(17-x) = dist from the landing point to the 17 mi point<BR>\n" );
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document.write( "Write a time equation; time = dist/speed<BR>\n" );
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document.write( "Rowing time + walking time = 4.75 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28x%5E2%2B9%5E2%29%29%2F4 ALIGN=MIDDLE  ALT=\"%28sqrt%28x%5E2%2B9%5E2%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2817-x%29%29%2F5 ALIGN=MIDDLE  ALT=\"%28%2817-x%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4.75<BR>\n" );
document.write( "multiply by 20 to clear the denominators, results:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28sqrt%28x%5E2%2B9%5E2%29%29 ALIGN=MIDDLE  ALT=\"5%28sqrt%28x%5E2%2B9%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 4(17-x) = 20(4.75)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28sqrt%28x%5E2%2B9%5E2%29%29 ALIGN=MIDDLE  ALT=\"5%28sqrt%28x%5E2%2B9%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 68 - 4x = 95<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28sqrt%28x%5E2%2B81%29%29%7D%7D+=+4x+%2B+95+-+68%0D%0A%3A%0D%0A%7B%7B%7B5%28sqrt%28x%5E2%2B81%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > = 4x + 27<BR>\n" );
document.write( "Square both sides, <BR>\n" );
document.write( "25(x^2 + 81) = 16x^2 + 216x + 729<BR>\n" );
document.write( "25x^2 + 2025 = 16x^2 + 216x + 729<BR>\n" );
document.write( "Combine like terms on the left<BR>\n" );
document.write( "25x^2 - 16x^2 - 216x + 2025 - 729 = 0<BR>\n" );
document.write( "9x^2 - 216x + 1296 = 0<BR>\n" );
document.write( "Simplify, divide by 9<BR>\n" );
document.write( "x^2 - 24x + 144 = 0<BR>\n" );
document.write( "Factors to <BR>\n" );
document.write( "(x - 12)(x - 12) = 0<BR>\n" );
document.write( "x = 12 miles from the opposite point to the landing point<BR>\n" );
document.write( ":<BR>\n" );
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document.write( "Check this out, find the rowing dist and walking dist<BR>\n" );
document.write( "Rowing dist = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2812%5E2%2B9%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2812%5E2%2B9%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 15 mi<BR>\n" );
document.write( "Walking dist = 17 - 12 = 5 mi<BR>\n" );
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document.write( "Find the times<BR>\n" );
document.write( "15/4 = 3.75 hrs rowing<BR>\n" );
document.write( "5/5  = 1.0 hr walking<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "total time 4.75 hrs<BR>\n" );
document.write( " </SPAN>\n" );
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