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 #816466 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=816466\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> what i get is the following.\r<BR>\n" );
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document.write( "rate * time = quantity.\r<BR>\n" );
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document.write( "the rate is the rate that the motor empties the tank per hour.<BR>\n" );
document.write( "the time is how long it takes to empty the tank.\r<BR>\n" );
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document.write( "the large motor empties the tank in 2 hours.<BR>\n" );
document.write( "rate * 2 = 1 empty tank.<BR>\n" );
document.write( "therefore, it is emptying 1/2 of the tank in one hour.\r<BR>\n" );
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document.write( "the small motor empties the tank in 4 hours.<BR>\n" );
document.write( "rate * 4 = 1 empty tank.<BR>\n" );
document.write( "therefore, it is emptying 1/4 of the tank in one hour.\r<BR>\n" );
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document.write( "when they work together, their rates are additive.<BR>\n" );
document.write( "you get (1/2 + 1/4) * time = 1 empty tank.<BR>\n" );
document.write( "combine fractions to get 3/4 * time = 1 empty tank.<BR>\n" );
document.write( "solve for time to get time = 4/3 hours.\r<BR>\n" );
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document.write( "you figure it has to be less than 2 hours because the little motor can empty the tank in 2 hours all by itself.<BR>\n" );
document.write( "with help from the big tank, the total time has to be less than 2 hours.\r<BR>\n" );
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document.write( "in 4/3 hours, the little motor empties 1/4 * 4/3 = 2/6 = 1/3 of the tank.<BR>\n" );
document.write( "in the same 4/3 hours, the large motor empties 1/2 * 4/3 = 4/6 = 2/3 of the tank.\r<BR>\n" );
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document.write( "their combined work empties 1/3 + 2/3 = 1 = all of the tank in 4/3 hours.\r<BR>\n" );
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document.write( "solution makes sense.\r<BR>\n" );
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document.write( "i would go with 4/3 hours to empty the tank when both motors are running.\r<BR>\n" );
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document.write( "if you let x equal the rate of the large motor and y equal the rate of the small motor, then your equations become:\r<BR>\n" );
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document.write( "x * 2 = 1 and y * 4 = 1.<BR>\n" );
document.write( "solve for the variables to get:<BR>\n" );
document.write( "x = 1/2 and y = 1/4\r<BR>\n" );
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document.write( "those are the rates that the large and small motors are emptying the tank.\r<BR>\n" );
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document.write( "hen they work together, the formula becomes:\r<BR>\n" );
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document.write( "(x + y) * T = 1\r<BR>\n" );
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document.write( "since x = 1/2 and y = 1/4, you get:<BR>\n" );
document.write( "(1/2 + 1/4) * T = 1<BR>\n" );
document.write( "solve for T to get T = 3/4 hours.\r<BR>\n" );
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document.write( "let me know if you need more information as to how this was done.\r<BR>\n" );
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document.write( "the rates of x and y are how much of the tank has been emptied in one hour.<BR>\n" );
document.write( "T is the time it takes to empty the tanks.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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