document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=725594>Question 725594</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I've been working on this problem and can only come up with an estimation, with no way of showing how I got there.<BR>\n" );
document.write( "A person is in a rowboat 3 miles from the closest point on a straight shoreline, as illustrated in the figure. The person would like to reach a cabin that is 8 miles down the shoreline. The person can row at 4 miles per hour and jog at 7 miles per hour.\r<BR>\n" );
document.write( "\n" );
document.write( " A.)How long will it take to reach the cabin if the person rows straight toward shore at point A and then jogs to the cabin?<BR>\n" );
document.write( "I estimated 1 hr. 50 minutes, but that is just a guess.<BR>\n" );
document.write( "B.) How long will it take to reach the cabin if the person rows straight to the cabin and does no jogging?<BR>\n" );
document.write( "C.)Find the minimum time to reach the cabin.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #444372 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=444372\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A person is in a rowboat 3 miles from the closest point on a straight shoreline, as illustrated in the figure.<BR>\n" );
document.write( " The person would like to reach a cabin that is 8 miles down the shoreline. The person can row at 4 miles per hour and jog at 7 miles per hour.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "A.)How long will it take to reach the cabin if the person rows straight toward shore at point A and then jogs to the cabin?<BR>\n" );
document.write( "A time equation: time = dist/speed<BR>\n" );
document.write( "total time (t)= row time + walk time<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4 ALIGN=MIDDLE  ALT=\"3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F7 ALIGN=MIDDLE  ALT=\"8%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = .75 + 1.143<BR>\n" );
document.write( "t 1.893 hrs or about 1 hr + .893(60) = 53.6 min<BR>\n" );
document.write( ":<BR>\n" );
document.write( "B.) How long will it take to reach the cabin if the person rows straight to the cabin and does no jogging?<BR>\n" );
document.write( "Solve this as a right triangle, direct to the cabin will be the hypotenuse<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%5E2%2B8%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%283%5E2%2B8%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "h = 8.544 miles<BR>\n" );
document.write( "Rowing at 4 mph: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8.544%2F4 ALIGN=MIDDLE  ALT=\"8.544%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2.136 hrs or about 2 hrs 8 min<BR>\n" );
document.write( ":<BR>\n" );
document.write( "C.)Find the minimum time to reach the cabin.<BR>\n" );
document.write( "This is a little more complicated. He will row to a point on the shore line, then jog from that point to the cabin.<BR>\n" );
document.write( " The position of the landing point has to be determined to find the rowing distance and the jogging distance that will yield the least total travel time><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let x = distance from the closest point on the shoreline to the landing point<BR>\n" );
document.write( "Then<BR>\n" );
document.write( "(8-x) = distance from the landing point to the cabin (the jogging distance)<BR>\n" );
document.write( "The rowing distance will be the hypotenuse of the triangle formed by x and 3<BR>\n" );
document.write( ":<BR>\n" );
document.write( "total time = rowing time + jogging time<BR>\n" );
document.write( "t(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28x%5E2%2B3%5E2%29%29%2F4 ALIGN=MIDDLE  ALT=\"%28sqrt%28x%5E2%2B3%5E2%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288-x%29%2F7 ALIGN=MIDDLE  ALT=\"%288-x%29%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Graphically<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-1%2C+5%2C+-1%2C+4%2C%28%28sqrt%28x%5E2%2B3%5E2%29%29%2F4%29%2B%288-x%29%2F7%29%29+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Minimum on the graph, x=2.1 mi from the closest point on shoreline, then<BR>\n" );
document.write( "Minimum time is when landing point is: 8-2.1 = 5.9 mi from the cabin<BR>\n" );
document.write( "Then it will take about 1.76 hrs to get to the cabin <BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check this<BR>\n" );
document.write( "find the rowing distance: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%5E2%2B2.1%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%283%5E2%2B2.1%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3.66 mi<BR>\n" );
document.write( "then 3.66/4 = .915 hrs rowing<BR>\n" );
document.write( "find the jogging distance: 8 - 2.1 = 5.9 mi<BR>\n" );
document.write( "then 5.9/7 = .843 hrs jogging<BR>\n" );
document.write( "Total time: .915 + .843 = 1.76 hrs min time to the cabin </SPAN>\n" );
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