document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1139720>Question 1139720</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Byron wanted to try out different water craft. He went 124 miles downstream in a motor boat and 45 miles downstream on a jet ski. His speed on the jet ski was 10 mph faster than in the motor boat. Byron spent a total of 4 hours on the water. What was his rate of speed, in miles per hour, in the motor boat?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #760240 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=760240\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rate * time = distance.\r<BR>\n" );
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document.write( "for the motor boat, r * t = 124.\r<BR>\n" );
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document.write( "for the speed boat, (r + 10) * (4 - t) = 45\r<BR>\n" );
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document.write( "r is the rate of the motorboat.<BR>\n" );
document.write( "r + 10 is the rate of the speed boat.\r<BR>\n" );
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document.write( "t is the time it takes the motorboat to travel 124 miles.<BR>\n" );
document.write( "4 - t is the time it takes the speedboat to travel 45 miles.\r<BR>\n" );
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document.write( "this is because the total time travel by both is 4 hours, so, if the motorboat took t hours, the speedboat had to take 4 - t hours.\r<BR>\n" );
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document.write( "you have 2 equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "r * t = 124<BR>\n" );
document.write( "(r + 10) * (4 - t) = 45\r<BR>\n" );
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document.write( "simplify the second equation and keep the first equation as is to get:\r<BR>\n" );
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document.write( "r * t = 124<BR>\n" );
document.write( "4 * r - r * t + 40 - 10 * t = 45\r<BR>\n" );
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document.write( "add the two equations together to get:\r<BR>\n" );
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document.write( "4 * r + 40 - 10 * t = 169\r<BR>\n" );
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document.write( "subtract 40 from both sides of the equation to get:\r<BR>\n" );
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document.write( "4 * r - 10 * t = 129\r<BR>\n" );
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document.write( "solve for r to get r = (10 * t + 129) / 4\r<BR>\n" );
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document.write( "in the first equation of r * t = 124, replace r with (10 * t + 129) / 4 to get:\r<BR>\n" );
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document.write( "(10 * t + 129) / 4 * t = 124\r<BR>\n" );
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document.write( "multiply both sides of that equation by 4 to get (10 * t + 129) * t = 496\r<BR>\n" );
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document.write( "simplify to get 10 * t^2 + 129 * t = 496\r<BR>\n" );
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document.write( "subtract 496 from both sides of that equation to get:\r<BR>\n" );
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document.write( "10 * t^2 + 129 * t - 496 = 0\r<BR>\n" );
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document.write( "factor this quadratic equation to get:\r<BR>\n" );
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document.write( "t = -16 or t = 3.1\r<BR>\n" );
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document.write( "t has to be greater than 0, so t = 3.1 looks like a possible solution.\r<BR>\n" );
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document.write( "in the first equation of r * t = 124, replace t with 3.1 and solve for r to get r = 124 / 3.1 which results in r = 40.\r<BR>\n" );
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document.write( "your solution should be t = 3.1 hours and r = 40 miles per hour.\r<BR>\n" );
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document.write( "for the motorboat, r * t = 124 becomes 40 * 3.1 = 124 which becomes 124 = 124 which confirms the solution is good for the first equation.\r<BR>\n" );
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document.write( "for the jet ski, (r + 10) * (4 - t) = 45 becomes 50 * .9 = 45 which becomes 45 = 45 which confirms the solution is good for the second equation.\r<BR>\n" );
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document.write( "the solution looks good.\r<BR>\n" );
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document.write( "the solution is that byron's rate of speed in the motorboat is 40 miles per hour.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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