document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=141890>Question 141890</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I refer to question number 139334 and question number 139296, both answerd by stanbon.\r<BR>\n" );
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document.write( "It takes Boat A 3 hours longer to travel 50kms than it takes Boat B to travel 60kms. Boat A travels one third the speed of Boat B. What is the speed of each boat.<BR>\n" );
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document.write( "A-Boat DATA:<BR>\n" );
document.write( "distance 50 km ; Rate = x kph ; time = 50/x<BR>\n" );
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document.write( "B-Boat DATA:<BR>\n" );
document.write( "distance = 60 km ; rate = 3x kph ; time = 60/(3x)<BR>\n" );
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document.write( "EQUATION:<BR>\n" );
document.write( "time A - time B = 3<BR>\n" );
document.write( "50/x - 60/(3x) = 3<BR>\n" );
document.write( "Multiply thru by 3x to get<BR>\n" );
document.write( "150 - 60 = 9x<BR>\n" );
document.write( "90 = 9x <BR>\n" );
document.write( "x = 10 kph (speed of A-Boat)<BR>\n" );
document.write( "3x = 30 kph (speed of B-Boat)<BR>\n" );
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document.write( "It takes a cabin cruiser 3 hours longer to travel 50kms than it takes a power boat to travel 60kms. The cruiser travels one third the speed of the power boat. Find the speed of each boat.  <BR>\n" );
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document.write( "Cruiser DATA:<BR>\n" );
document.write( "distance = 50 km ; rate = x kph ; time = 50/x hrs<BR>\n" );
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document.write( "Power Boat DATA:<BR>\n" );
document.write( "distance = 60 km ; rate = 3x kph ; time = 60/(3x) hrs<BR>\n" );
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document.write( "EQUATION:<BR>\n" );
document.write( "cruise time = power boat time + 3 hrs.<BR>\n" );
document.write( "50/x = 60/3x + 3<BR>\n" );
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document.write( "Multiply thru by 3x to get:<BR>\n" );
document.write( "150 = 60 + 9x<BR>\n" );
document.write( "210 = 9x <BR>\n" );
document.write( "x = 70/3 = 23 1/3 kph (cruiser speed)<BR>\n" );
document.write( "3x = 70 kph (power boat speed)<BR>\n" );
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document.write( "The questions are identical, save for the description of the boats, yet the answers are different.\r<BR>\n" );
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document.write( "Please confirm the answer to the second question is correct ...... I would have thought the equation should have read:\r<BR>\n" );
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document.write( "Multiply thru by 3x to get:<BR>\n" );
document.write( "150 = 60 + 9x<BR>\n" );
document.write( "90 = 9x <BR>\n" );
document.write( "x = 90/9 = 10 kph (cruiser speed)<BR>\n" );
document.write( "3x = 10*3 = 30 kph (power boat speed)\r<BR>\n" );
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document.write( "Thanks\r<BR>\n" );
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document.write( "George<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 #103363 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=103363\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Distance(d) equals Rate(r) times Time(t) or d=rt;  r=d/t and t=d/r\r<BR>\n" );
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document.write( "Let r=rate (speed) of Boat B<BR>\n" );
document.write( "Then r/3=speed of Boat A\r<BR>\n" );
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document.write( "Time required for boat B to travel 60 km=60/r<BR>\n" );
document.write( "Time required for Boat A to travel 50 km=50/(r/3)=150/r\r<BR>\n" );
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document.write( "And we are told that Boat A's time is 3 hours longer than Boat B's time, so:\r<BR>\n" );
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document.write( "150/r=(60/r)+3  multiply each term by r\r<BR>\n" );
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document.write( "150=60+3r  subtract 60 from each side<BR>\n" );
document.write( "150-60=60-60+3r collect like terms<BR>\n" );
document.write( "90=3r  divide each side by 3<BR>\n" );
document.write( "r=30 km/h----------------------------------------speed of Boat B\r<BR>\n" );
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document.write( "r/3=30/3=10 km/h----------------------------------speed of Boat A\r<BR>\n" );
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document.write( "CK<BR>\n" );
document.write( "50/10=60/30+3<BR>\n" );
document.write( "5=2+3<BR>\n" );
document.write( "5=5\r<BR>\n" );
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document.write( "Hope this helps---ptaylor </SPAN>\n" );
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