document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=74258>Question 74258</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can you help me in solving the problem...\r<BR>\n" );
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document.write( "ariana took 2 h longer to drive 360 mi on the first day of a trip than she took to drive 270 mi on the second day.  if her speed was the same on both days, what was the driving time each day? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #53263 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=53263\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We're going to use the equation that says Distance (D) is equal to the Rate (R) times the Time (T)<BR>\n" );
document.write( "or in equation form:<BR>\n" );
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document.write( "D = R*T<BR>\n" );
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document.write( "On the second day she drove 270 miles in the time T. In equation form this is:<BR>\n" );
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document.write( "270 = R*T<BR>\n" );
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document.write( "Solve this equation for R by dividing both sides by T to get R = 270/T<BR>\n" );
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document.write( "On the first day she drove 360 miles in the time T+2.  In equation form this is:<BR>\n" );
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document.write( "360 = R*(T+2)<BR>\n" );
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document.write( "Solve this equation for R by dividing both sides by (T+2) to get R = 360/(T+2)<BR>\n" );
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document.write( "The problem then says the R is the same on both days. Since it equals 360/(T+2) on the<BR>\n" );
document.write( "first day and 270/T on the second day we can set these two equal to get:<BR>\n" );
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document.write( "360/(T+2) = 270/T<BR>\n" );
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document.write( "Multiply both sides by (T+2) to get rid of the denominator on the left side and you get:<BR>\n" );
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document.write( "360 = 270*(T+2)/T<BR>\n" );
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document.write( "Then multiply both sides by T to get rid of the denominator on the right side.  The equation becomes:<BR>\n" );
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document.write( "360T = 270*(T+2)<BR>\n" );
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document.write( "Multiply out the right side and the equation further becomes:<BR>\n" );
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document.write( "360T = 270T + 540<BR>\n" );
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document.write( "Next get rid of the 270T on the right side by subtracting 270 from both sides of the equation:<BR>\n" );
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document.write( "90T = 540<BR>\n" );
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document.write( "Now you can solve for T by dividing both sides of the equation by 90 and the result is:<BR>\n" );
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document.write( "T = 540/90 = 6<BR>\n" );
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document.write( "So the time (T) which is the driving time on the second day is 6 hours.  That means that<BR>\n" );
document.write( "on the first day she drove 2 additional hours for a total driving time on the first day <BR>\n" );
document.write( "of 8 hours.<BR>\n" );
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document.write( "Another and quicker way you could have done this problem is to say that that on the first<BR>\n" );
document.write( "day she spent 2 more hours on the road and she drove 90 more miles (360 miles on that day<BR>\n" );
document.write( "and 270 miles on the second day).  So in those 2 hours she averaged 45 miles per hour to cover<BR>\n" );
document.write( "those 90 miles in 2 hours.  So at 45 miles per hour it would take 8 hours to cover the <BR>\n" );
document.write( "360 miles.  On the second day she still drove at 45 mph and to cover 270 miles divide 270 by 45<BR>\n" );
document.write( "and find that it took 6 hours.  <BR>\n" );
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document.write( "Hope these two approaches to solving the problem give you some insight into the relationship<BR>\n" );
document.write( "among distance, rate, and time.<BR>\n" );
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