document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=106551>Question 106551</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two-way radio range:\r<BR>\n" );
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document.write( "Two surveyors with two-way radios leave the same point at 9:00AM, one walking due south at 4 mi/hr and the other due west at 3 mi/hr.  How long can they communicate with one another if each radio has a maximum range of 2 miles? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #77557 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=77557\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two surveyors with two-way radios leave the same point at 9:00AM, one walking due south at 4 mi/hr and the other due west at 3 mi/hr.  How long can they communicate with one another if each radio has a maximum range of 2 miles?<BR>\n" );
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document.write( "They cancommunicate until they are 4 miles from one-another<BR>\n" );
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document.write( "Draw the picture with one going south at 4mph, the other going west at 3 mph.<BR>\n" );
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document.write( "Let the one going west go a distance of \"x\" miles<BR>\n" );
document.write( "Draw a line segment from his position to the postion of the southbound<BR>\n" );
document.write( "person.  Make the length of that segment be \"4\"<BR>\n" );
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document.write( "Then, using Pythagoras, the distance the southbound person has gon is <BR>\n" );
document.write( "sqrt(4^2-x^2) = sqrt(16-x^2) miles.<BR>\n" );
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document.write( "EQUATION:<BR>\n" );
document.write( "Time = distance/rate<BR>\n" );
document.write( "Westbound person time = x/3 hr<BR>\n" );
document.write( "southbound person time = [sqrt(16-x^2)]/4<BR>\n" );
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document.write( "west time = south time<BR>\n" );
document.write( "x/3 = [sqrt(16-x^2)]/4<BR>\n" );
document.write( "4x = 3[sqrt(16-x^2)]<BR>\n" );
document.write( "Square both sides to get:<BR>\n" );
document.write( "16x^2 = 9(16-x^2)<BR>\n" );
document.write( "16x^2 = 144 - 9x^2<BR>\n" );
document.write( "25x^2 = 144<BR>\n" );
document.write( "x = 12/5 = 2.4 miles (distance westbound person goes.<BR>\n" );
document.write( "2.4/3 = 0.8 hrs (time the westbound person goes)<BR>\n" );
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document.write( "Their maximum communication time is 0.8 hrs.  = 48 minutes<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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