document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=453838>Question 453838</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A scientist wants to go to a small island 5km south of the coastline and<BR>\n" );
document.write( "13km from the town. From town, he drives his small truck east along the<BR>\n" );
document.write( "waterfront, towing his boat. Then he parks his truck, and travels straight to<BR>\n" );
document.write( "the island by boat.\r<BR>\n" );
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document.write( "(a) The truck travels at 50km/h. The boat travels at 20km/h. How far east<BR>\n" );
document.write( "of town should he park his truck and start his boat journey to minimize<BR>\n" );
document.write( "the travel time? \r<BR>\n" );
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document.write( "(b) The truck uses $1 of diesel per km travelled, while the boat uses 60c of<BR>\n" );
document.write( "diesel per km. What should the scientist do if he wants to minimize the<BR>\n" );
document.write( "cost? <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #311855 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=311855\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A scientist wants to go to a small island 5km south of the coastline and<BR>\n" );
document.write( "13km from the town.<BR>\n" );
document.write( " From town, he drives his small truck east along the waterfront, towing his boat.<BR>\n" );
document.write( " Then he parks his truck, and travels straight to the island by boat.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "(a) The truck travels at 50km/h. The boat travels at 20km/h.<BR>\n" );
document.write( " How far east of town should he park his truck and start his boat journey to minimize the travel time?<BR>\n" );
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document.write( "Find the distance (d) to the point on the shore just north of the island<BR>\n" );
document.write( "d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2813%5E2-5%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2813%5E2-5%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d = 12 km to a point on the shore due north of the island, (from the town)<BR>\n" );
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document.write( "Let p = distance to point on the shore east of town to launch the boat<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(12-p) = distance from that point to a point due north of the island<BR>\n" );
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document.write( "The boat route to the island is the hypotenuse of a right angle where:<BR>\n" );
document.write( "a = 5<BR>\n" );
document.write( "b = (12-p)<BR>\n" );
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document.write( "Write a time equation, time = dist/speed<BR>\n" );
document.write( "total time (t) for the truck and boat<BR>\n" );
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document.write( "total time = truck time + boat time<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2F50 ALIGN=MIDDLE  ALT=\"p%2F50\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%285%5E2%2B%2812-p%29%5E2%29%29%2F20 ALIGN=MIDDLE  ALT=\"%28sqrt%285%5E2%2B%2812-p%29%5E2%29%29%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2F50 ALIGN=MIDDLE  ALT=\"p%2F50\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%2825%2B%28144-24p+%2B+p%5E2%29%29%29%2F20 ALIGN=MIDDLE  ALT=\"%28sqrt%2825%2B%28144-24p+%2B+p%5E2%29%29%29%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2F50 ALIGN=MIDDLE  ALT=\"p%2F50\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%2825%2B144-24p+%2B+p%5E2%29%29%2F20 ALIGN=MIDDLE  ALT=\"%28sqrt%2825%2B144-24p+%2B+p%5E2%29%29%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2F50 ALIGN=MIDDLE  ALT=\"p%2F50\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28p%5E2-24p%2B169%29%29%2F20 ALIGN=MIDDLE  ALT=\"%28sqrt%28p%5E2-24p%2B169%29%29%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Graphing this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+20%2C+-.5%2C+1%2C+%28x%2F50%29%2Bsqrt%28x%5E2-24x%2B169%29%2F20%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "total travel time minimum occurs when:<BR>\n" );
document.write( " p = 9.8 km by truck to a point east of town, launch the boat there<BR>\n" );
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document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "(b) The truck uses $1 of diesel per km traveled, while the boat uses 60c of<BR>\n" );
document.write( "diesel per km.<BR>\n" );
document.write( " What should the scientist do if he wants to minimize the cost.<BR>\n" );
document.write( "Modify the equation to:<BR>\n" );
document.write( "Cost = 1p + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.6%2Asqrt%28p%5E2-24p%2B169%29 ALIGN=MIDDLE  ALT=\".6%2Asqrt%28p%5E2-24p%2B169%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Graph this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+x%2B.6sqrt%28x%5E2-24x%2B169%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+x%2B.6sqrt%28x%5E2-24x%2B169%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It appears he should not drive the truck at all but travel all the way by boat (p=0).<BR>\n" );
document.write( "His expense the will be 13*.6 = $7.80, will increase for each km he drives the truck </SPAN>\n" );
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