document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1145867>Question 1145867</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man in a rowboat that is a = 4 miles from the nearest point A on a straight shoreline wishes to reach a house located at a point B that is b = 10 miles farther down the shoreline. He plans to row to a point P that is between A and B and is x miles from the house, and then he will walk the remainder of the distance.\r<BR>\n" );
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document.write( "Suppose he can row at a rate of 3 mi/hr and can walk at a rate of 5 mi/hr. If T is the total time required to reach the house, express T as a function of x.<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 #767149 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=767149\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> my understanding of this problem is shown in the following diagram.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/092701.jpg\"alt=\"$$$\">\r<BR>\n" );
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document.write( "the rowboat is at point R.<BR>\n" );
document.write( "the shorted distance point on the shore if point A.<BR>\n" );
document.write( "the hours is at point B.\r<BR>\n" );
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document.write( "the distance from the rowboat to point A is 4 miles which is the length of line RA.\r<BR>\n" );
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document.write( "the distance from point A to the house at point B is 10 miles which is the length of line AB\r<BR>\n" );
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document.write( "the distance from point P to the house at point B is x miles which is the length of line PB.\r<BR>\n" );
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document.write( "this makes the distance from point A to point P equal to (10 - x).\r<BR>\n" );
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document.write( "the distance from the rowboat to point P is equal to the hypotenuse of the right triangle RAP which is the line RP.\r<BR>\n" );
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document.write( "that makes the distance equal to sqrt(4^2 + (10-x)^2).\r<BR>\n" );
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document.write( "simplify that to get distance from point A to P equal to sqrt(x^2-20x+116).\r<BR>\n" );
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document.write( "the basic formula to use is r * t = d<BR>\n" );
document.write( "r is the rate.<BR>\n" );
document.write( "t is the time.<BR>\n" );
document.write( "d is the distance.\r<BR>\n" );
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document.write( "the man rows the boat at 3 miles per hour.<BR>\n" );
document.write( "the man walks at 5 miles per hour.\r<BR>\n" );
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document.write( "let T1 equal the time it takes to get from point R to point P rowing the boat.<BR>\n" );
document.write( "let D1 equal the distance from point R to point P.<BR>\n" );
document.write( "you get r * t = d becomes 3 * T1 = D1<BR>\n" );
document.write( "since D1 = sqrt(x^2-20x+116), you get 3 * T1 = sqrt(x^2-20x+116)<BR>\n" );
document.write( "solve for T1 to get T1 = sqrt(x^2-20x+116)/3\r<BR>\n" );
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document.write( "let T2 equal the time it takes to get from poinnt P to point B walking.<BR>\n" );
document.write( "let D2 equal the distance from point P to point B.<BR>\n" );
document.write( "you get r * t = d becomes 5 * T2 = D2<BR>\n" );
document.write( "since D2 = x, you get 5 * T2 = x<BR>\n" );
document.write( "solve for T2 to get T2 = x/5\r<BR>\n" );
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document.write( "let the total time it takes to get from point R to point B through point P equal to T.<BR>\n" );
document.write( "you get T = T1 + T2 = sqrt(x^2-20x+116)/3 + x/5\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "you can combine that equation into one common denominator to get:\r<BR>\n" );
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document.write( "T = (5*sqrt(x^2-20x+116) + 3x)/15\r<BR>\n" );
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document.write( "the two equations of T, shown above, are equivalent.<BR>\n" );
document.write( "they produce the same value for T.\r<BR>\n" );
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document.write( "the domain of the T function is 0 < x < 10, where x represents the distance from point P to point B.\r<BR>\n" );
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document.write( "x cannot be 0 because then point P would be the same point as point B.<BR>\n" );
document.write( "x cannot be 10 because then point P would be the same point as point A.\r<BR>\n" );
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document.write( "that's because the problem statement says that point P is between point A and point B and can therefore not be at either of them.\r<BR>\n" );
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document.write( "either of the equations involving T will be your solution, depending on how you want to show them.\r<BR>\n" );
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