document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=152566>Question 152566</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this: Clifford \"TI\" Harris went on a weekend trip. He averaged 35mi/h in the city and 60mi/h on the highway. If the 150mi trip took 3hrs, how much of the time was he driving in the city. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #112184 by </B><A HREF=/tutors/aboutme.mpl?userid=mducky2><B>mducky2(62)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mducky2><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=112184\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>Here are some equations that might help us.<BR>\n" );
document.write( "Speed * Time = Distance<BR>\n" );
document.write( "Time = Distance/Speed<BR>\n" );
document.write( "Speed = Distance/Time<BR>\n" );
document.write( "<br>For ease of labeling, let's label time, distance, and speed with variables:<BR>\n" );
document.write( "T = time<BR>\n" );
document.write( "D = distance<BR>\n" );
document.write( "S = speed<BR>\n" );
document.write( "<br>Now let's figure out what information the problem gives us.<BR>\n" );
document.write( "speed in city = S<sub>c</sub> = 35 mph<BR>\n" );
document.write( "speed on highway = S<sub>h</sub> = 60 mph<BR>\n" );
document.write( "total time = T<sub>total</sub> = 3 hours<BR>\n" );
document.write( "total distance = D<sub>total</sub> = 150 miles<BR>\n" );
document.write( "<br>It looks like we can use the first equation to help us. The speed times the time on the city equals the distance in the city. The speed times the time on the highway equals the distance on the highway. Adding the two together should give us the total distance:<BR>\n" );
document.write( "Speed * Time = Distance<BR>\n" );
document.write( "S<sub>c</sub>*T<sub>c</sub> = D<sub>c</sub><BR>\n" );
document.write( "S<sub>h</sub>*T<sub>h</sub> = D<sub>h</sub><BR>\n" );
document.write( "S<sub>c</sub>T<sub>c</sub>+S<sub>h</sub>T<sub>h</sub> = D<sub>total</sub><BR>\n" );
document.write( "35T<sub>c</sub> + 60T<sub>h</sub> = 150<BR>\n" );
document.write( "<br>Since we know the total time, we can solve for the time in the highway in terms of the time in the city:<BR>\n" );
document.write( "T<sub>c</sub> + T<sub>h</sub> = 3<BR>\n" );
document.write( "T<sub>h</sub> = 3 - T<sub>c</sub><BR>\n" );
document.write( "<br>Plugging back into the original equation:<BR>\n" );
document.write( "35t<sub>c</sub> + 60(3 - t<sub>c</sub>) = 150<BR>\n" );
document.write( "35t<sub>c</sub> + 180 - 60t<sub>c</sub>) = 150<BR>\n" );
document.write( "180 - 25T<sub>c</sub> = 150<BR>\n" );
document.write( "180 - 150 = 25T<sub>c</sub><BR>\n" );
document.write( "30 = 25T<sub>c</sub><BR>\n" );
document.write( "T<sub>c</sub> = 30/25<BR>\n" );
document.write( "T<sub>c</sub> = 6/5 hrs<BR>\n" );
document.write( "T<sub>c</sub> = 1 hr and 12 minutes<BR>\n" );
document.write( "<br>Clifford \"TI\" Harris spent 1 hr and 12 minutes driving in the city.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );