document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185630>Question 1185630</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a word problem here and I having trouble figuring out the let statements and equations to solve the problem. The word problem is:\r<BR>\n" );
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document.write( "A boat has two motors, one large and one small. If only the large motor is running. a tank of fuel lasts 2 h. If only the small motor is running, the tank of fuel lasts 4 h.\r<BR>\n" );
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document.write( "How long will the fuel last if both motors are running? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #816475 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=816475\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The question as posted asks the student to use an appropriate \"let\" statement and equation(s) to solve the problem.  The number asked for is the number of hours the tank of fuel will last if both motors are running, so that is the logical choice for the variable.<br><BR>\n" );
document.write( "Let x = # of hours the tank of fuel lasts if both motors are running.<br><BR>\n" );
document.write( "This is a variation of a standard \"working together\" problem; the standard algebraic solution method is to work with the fractions of the job the two workers do individually and together.  For this problem, the \"job\" is emptying the fuel tank.<br><BR>\n" );
document.write( "1/4 = fraction of the job the small motor does in 1 hour<BR>\n" );
document.write( "1/2 = fraction of the job the large motor does in 1 hour<BR>\n" );
document.write( "1/x = fraction of the job the two motors together do in 1 hour<br><BR>\n" );
document.write( "Logically, then, the equation for solving the problem says the fraction of the job done in 1 hour is the sum of the fractions of the job done by each motor in 1 hour:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4%2B1%2F2=1%2Fx ALIGN=MIDDLE  ALT=\"1%2F4%2B1%2F2=1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Start solving the equation by multiplying everything by the least common denominator, 4x:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2x=4 ALIGN=MIDDLE  ALT=\"x%2B2x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=4 ALIGN=MIDDLE  ALT=\"3x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4%2F3 ALIGN=MIDDLE  ALT=\"x=4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: The two motors running together take 4/3 hours, or 1 1/3 hours, or 1 hour 20 minutes, to empty the fuel tank<br><BR>\n" );
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