document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=826357>Question 826357</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you need to move many tonnes of gravel and you have two trucks available. One truck is capable of completing the job in 15 trips, while the other truck is capable of completing the job in 25 trips.To solve the following questions, notice that one truck completes 1/15 of the job each trip and the other truck completes 1/25 of the job each trip.<BR>\n" );
document.write( "a. How much of the job is completed if the two trucks make one trip together?<BR>\n" );
document.write( "b. How many trips are required to complete the job if the two trucks travel together?<BR>\n" );
document.write( "c. Suppose that one truck can complete the job in (n) trips and the other truck can complete the job in 120 trips. Write an equation to represent the total number of trips, (T), required if the two trucks work together.<BR>\n" );
document.write( "d. If 55 trips are required when the two trucks in question c. work together, how many trips would it take for the first truck to complete the job alone? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #498037 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=498037\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One truck is capable of completing the job in 15 trips, while the other truck is capable of completing the job in 25 trips.<BR>\n" );
document.write( "To solve the following questions, notice that one truck completes 1/15 of the job each trip and the other truck completes 1/25 of the job each trip.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "a. How much of the job is completed if the two trucks make one trip together?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F15 ALIGN=MIDDLE  ALT=\"1%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F25 ALIGN=MIDDLE  ALT=\"1%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <BR>\n" );
document.write( "The common denominator is 75<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F75 ALIGN=MIDDLE  ALT=\"5%2F75\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F75 ALIGN=MIDDLE  ALT=\"3%2F75\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F75 ALIGN=MIDDLE  ALT=\"8%2F75\"   DISABLED_style= \"max-width:90%; height:auto;\" > * 100 = 10.67% completed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "b. How many trips are required to complete the job if the two trucks travel together?<BR>\n" );
document.write( "Let t = no. of trips to complete job<BR>\n" );
document.write( "Let the completed job = 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2F15 ALIGN=MIDDLE  ALT=\"t%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2F25 ALIGN=MIDDLE  ALT=\"t%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "multiply equation by 75 to clear the denominators<BR>\n" );
document.write( "5t + 3t = 75<BR>\n" );
document.write( "8t = 75<BR>\n" );
document.write( "t = 75/8<BR>\n" );
document.write( "t = 9.375 ~ 10 trips of the two trucks required<BR>\n" );
document.write( "However in the interest of economy, have the smaller truck make 10 trips<BR>\n" );
document.write( "and larger truck make 9 trips<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F15 ALIGN=MIDDLE  ALT=\"9%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F25 ALIGN=MIDDLE  ALT=\"10%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F5 ALIGN=MIDDLE  ALT=\"3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F5 ALIGN=MIDDLE  ALT=\"2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1, exactly a complete job<BR>\n" );
document.write( ":<BR>\n" );
document.write( "c. Suppose that one truck can complete the job in (n) trips and the other truck can complete the job in 120 trips.<BR>\n" );
document.write( " Write an equation to represent the total number of trips, (T), required if the two trucks work together.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2Fn ALIGN=MIDDLE  ALT=\"t%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2F120 ALIGN=MIDDLE  ALT=\"t%2F120\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "multiply by 120n, results:<BR>\n" );
document.write( "120t + tn = 120n<BR>\n" );
document.write( "t(120+n) = 120n<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28120n%29%2F%28120%2Bn%29 ALIGN=MIDDLE  ALT=\"%28120n%29%2F%28120%2Bn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "d. If 55 trips are required when the two trucks in question c. work together, how many trips would it take for the first truck to complete the job alone?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28120n%29%2F%28120%2Bn%29 ALIGN=MIDDLE  ALT=\"%28120n%29%2F%28120%2Bn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 55<BR>\n" );
document.write( "120n = 55(120+n)<BR>\n" );
document.write( "120n = 6600 + 55n<BR>\n" );
document.write( "120n - 55n = 6600<BR>\n" );
document.write( "65n = 6600<BR>\n" );
document.write( "n = 6600/65<BR>\n" );
document.write( "n ~ 101 trips for the 1st truck alone<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55%2F101 ALIGN=MIDDLE  ALT=\"55%2F101\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55%2F120 ALIGN=MIDDLE  ALT=\"55%2F120\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.00, a complete job </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );