document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1167287>Question 1167287</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A train travel from Tutuban to Calamba station. The distance between Tutuban and Calamba is defined by the function 𝑑(𝑥) = 𝑥4 + 𝑥3+ 3𝑥2 + 4𝑥 − 𝑥 kilometers. If the train travels from Tutuban to Calamba for 𝑡(𝑥) = 𝑥 hours without stopping at any station, do you think if the speed of this train will be 45 km/h, will it arrive on its destination for only 2 hours?  \r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #791916 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=791916\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i'm not sure if this is right, but i'll give it a shot, based on my understanding of the problem, or lack thereof.\r<BR>\n" );
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document.write( "you are given that:\r<BR>\n" );
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document.write( "d(x) = x^4 + x^3 + 3x^2 + 4x - x kilometers.\r<BR>\n" );
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document.write( "t(x) = x\r<BR>\n" );
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document.write( "presumably the same value of x is used in both equations.\r<BR>\n" );
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document.write( "what i think this means is, the distance traveled is a function of time traveled, and that this relationship is preserved for any given speed.\r<BR>\n" );
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document.write( "the formula i think you would want to use is:\r<BR>\n" );
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document.write( "r * t = d\r<BR>\n" );
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document.write( "r is the rate in kilometers per hour.<BR>\n" );
document.write( "t is the time in hours.<BR>\n" );
document.write( "d is the distance in hours.\r<BR>\n" );
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document.write( "based on the formulas you are given, this becomes:\r<BR>\n" );
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document.write( "r * t(x) = d(x)\r<BR>\n" );
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document.write( "if the train travels for 2 hours, then:\r<BR>\n" );
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document.write( "t(x) = x becomes t(2) = 2\r<BR>\n" );
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document.write( "d(x) = x^4 + x^3 + 3x^2 + 4x - x becomes d(2) = 2^4 + 2^3 + 3*2^2 + 4*2 - 2 which becomes d(2) = 42.\r<BR>\n" );
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document.write( "you have t(2) = 2 and d(2) = 42\r<BR>\n" );
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document.write( "if the trip takes 2 hours, then the distance traveled is 42 kilometers based on the value of x = 2 in both equations.\r<BR>\n" );
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document.write( "the rate * time = distance equation of r * t(x) = d(x) becomes:\r<BR>\n" );
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document.write( "r * 2 = 42\r<BR>\n" );
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document.write( "solve for r to get:\r<BR>\n" );
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document.write( "r = 42/2 = 21.\r<BR>\n" );
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document.write( "this says the train will travel 42 kilometers in 2 hours if the train travels at 21 kilometers per hour.\r<BR>\n" );
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document.write( "since 21 kilometers per hour is slower than 45 kilometers per hour, the train should make it in plenty of time.\r<BR>\n" );
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document.write( "in fact, assuming the distance is 42 kilometers and the train is traveling at 45 kilometers per hour, then the train will make the trip in 42/45 of an hour.\r<BR>\n" );
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document.write( "multiply this by 60 to find that the train travels for 56 minutes to go 42 miles.\r<BR>\n" );
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document.write( "i believe your solution is that the train will definitely make the trip in less than 2 hours with plenty of time to spare, based on my understanding of the problem.\r<BR>\n" );
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