document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=313345>Question 313345</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Please help me solve this  <BR>\n" );
document.write( "2 boats are 110 km apart they travel towards each others one traveling at 5km/hr slower than other if they in 2hr find the speed of each boat </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #224060 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=224060\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2 boats are 110 km apart.<BR>\n" );
document.write( "They travel toards each other.<BR>\n" );
document.write( "Boat 1 travels 5 km/hr slower than the other.<BR>\n" );
document.write( "They meet in 2 hours.<BR>\n" );
document.write( "What is the speed of each boat.\r<BR>\n" );
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document.write( "This problem deals with R*T = D which means:\r<BR>\n" );
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document.write( "Rate (otherwise known as speed) times Time equals Distance.\r<BR>\n" );
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document.write( "If I travel for 1 hour at 50 miles an hour, then I will have traveled 100 miles in 2 hours.\r<BR>\n" );
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document.write( "R*T = D becomes 50*2 = 100\r<BR>\n" );
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document.write( "In your problem, we let x equal the speed of boat 1.\r<BR>\n" );
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document.write( "Since boat 1 is traveling 5 km/hr slower than boat 2, the speed of boat 2 must be equal to X + 5.\r<BR>\n" );
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document.write( "Boat 1 travels at x km per hour.<BR>\n" );
document.write( "Boat 2 travels at (x+5)  km per hour.\r<BR>\n" );
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document.write( "The total distance that both boats travel is 120 km.\r<BR>\n" );
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document.write( "They will meet at some point in the middle.\r<BR>\n" );
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document.write( "The total time that each boat takes is 2 hours since they are both traveling at the same time.\r<BR>\n" );
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document.write( "The formula for boat 1 becomes:\r<BR>\n" );
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document.write( "x * 2 = y\r<BR>\n" );
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document.write( "We use y for the distance since we don't know how far boat 1 has traveled.\r<BR>\n" );
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document.write( "The formula for boat 2 becomes:\r<BR>\n" );
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document.write( "(x + 5) * 2 = z\r<BR>\n" );
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document.write( "We use z for the distance since we don't know how far boat 2 has traveled, only we know that it's not the same distance that boat 1 has traveled.\r<BR>\n" );
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document.write( "y is the distance that boat 1 travels.<BR>\n" );
document.write( "z is the distance that boat 2 travels.\r<BR>\n" );
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document.write( "We know that y + z = 110 km because we know that the total distance traveled by both boats is equal to 110 km.\r<BR>\n" );
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document.write( "From the Formula of y + z = 110, we can derive y in terms of z, or z in terms of y.\r<BR>\n" );
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document.write( "We'll solve for y in terms of z to get y = 110 - z.\r<BR>\n" );
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document.write( "This allows us to eliminate y as a variable in the equation.\r<BR>\n" );
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document.write( "Our formulas for boat 1 and boat 2 that were:\r<BR>\n" );
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document.write( "x * 2 = y<BR>\n" );
document.write( "(x + 5) * 2 = z\r<BR>\n" );
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document.write( "become:\r<BR>\n" );
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document.write( "x * 2 = 110 - z<BR>\n" );
document.write( "(x + 5) * 2 = z\r<BR>\n" );
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document.write( "We will solve both formulas for z which will allow us to eliminate z as a variable in the equation.\r<BR>\n" );
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document.write( "The second formula is already solved for z.\r<BR>\n" );
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document.write( "The first formula is:\r<BR>\n" );
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document.write( "x * 2 = 110 - z.\r<BR>\n" );
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document.write( "Add z to both sides of this equation and subtract (x * 2) from both sides of this equation to get:\r<BR>\n" );
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document.write( "z = 110 - (x * 2)\r<BR>\n" );
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document.write( "We now have solved for z in 2 equations.\r<BR>\n" );
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document.write( "They are:\r<BR>\n" );
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document.write( "z = 110 - x*2<BR>\n" );
document.write( "z = (x+5) * 2\r<BR>\n" );
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document.write( "Since both expressions on the right side of each equation are equal to z, we can set both expressions equal to each other to get:\r<BR>\n" );
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document.write( "110 - x*2 = (x+5) * 2\r<BR>\n" );
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document.write( "We have now eliminated z as a variable in the equation.\r<BR>\n" );
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document.write( "We now have one equation in one unknown which can be solved.\r<BR>\n" );
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document.write( "Add x*2 to both sides of this equation to get:\r<BR>\n" );
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document.write( "110 = (x+5)*2 + x*2\r<BR>\n" );
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document.write( "Simplify this equation by removing parentheses to get:\r<BR>\n" );
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document.write( "110 = 2*x + 2*5 + 2*x\r<BR>\n" );
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document.write( "Combine like terms and simplify further to get:\r<BR>\n" );
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document.write( "110 = 4*x + 10\r<BR>\n" );
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document.write( "Subtract 10 from both sides of this equation to get:\r<BR>\n" );
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document.write( "4*x = 100\r<BR>\n" );
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document.write( "Divide both sides of the equation by 4 to get:\r<BR>\n" );
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document.write( "x = 25\r<BR>\n" );
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document.write( "If x = 25, then (x+5) must equal to 30\r<BR>\n" );
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document.write( "Boat 1 is traveling at x = 25 km per hour.<BR>\n" );
document.write( "Boat 2 is traveling at (x+5) = 30 km per hour.\r<BR>\n" );
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document.write( "We test out answer to see if it is correct.\r<BR>\n" );
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document.write( "Boat 1 travels 25 km per hour for 2 hours which means boat 1 has traveled 50 km.\r<BR>\n" );
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document.write( "Boat 2 travels 30 km per hour for 2 hours which means boat 2 has traveled 60 km.\r<BR>\n" );
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document.write( "50 km + 60 km = 110 km which is the total distance traveled by both boats.\r<BR>\n" );
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document.write( "If they start 110 km apart, they will meet in exactly 2 hours when boat 1 has traveled 50 km and boat 2 has traveled 60 km.\r<BR>\n" );
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document.write( "The answer to your question is:\r<BR>\n" );
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document.write( "Boat 1 travels at 25 km per hour.<BR>\n" );
document.write( "Boat 2 travels at 30 km per hour.\r<BR>\n" );
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document.write( "the key to solving this problem is determining equivalencies and reducing the number of unknowns.\r<BR>\n" );
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document.write( "Knowing that y + z = 110 allows you to solve for y in terms of z or z in terms of y which eliminates one of the unknowns.  In our case, we eliminated z as an unknown.\r<BR>\n" );
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document.write( "Setting both equations equal to z and then setting the equations equal to each other allows you to eliminate another of the unknowns.   The unknown we we eliminated was z.\r<BR>\n" );
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document.write( "Once you're down to one unknown in one equation, solving becomes just a matter of working through the details.\r<BR>\n" );
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document.write( "You also need to know the basics of the type of problem which is:\r<BR>\n" );
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document.write( "Rate * Time = Distance\r<BR>\n" );
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document.write( "This problem could not be solved without knowing that.\r<BR>\n" );
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