document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=581527>Question 581527</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The train from C to D breaks down after 1 hour. The train has stopped because of 1/2 hour repairs, then,  it continues on at 3/4 of its beginning rate, arriving at B 2 hours late. If the train had covered 75 miles more before the break down, it could be only1 hour late. What is the beginning rate of the train? Explain how you would get the answer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #371750 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=371750\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The train from C to D breaks down after 1 hour.<BR>\n" );
document.write( " The train has stopped because of 1/2 hour repairs, then, it continues on at 3/4 of its beginning rate, arriving at B 2 hours late.<BR>\n" );
document.write( " If the train had covered 75 miles more before the break down, it could be only 1 hour late.<BR>\n" );
document.write( " What is the beginning rate of the train? Explain how you would get the answer.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let s = original speed of the train, also distance traveled in 1 hr<BR>\n" );
document.write( "then<BR>\n" );
document.write( ".75s = speed after the breakdown<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let d = distance from C to D<BR>\n" );
document.write( "then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fs ALIGN=MIDDLE  ALT=\"d%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > the normal time for the trip<BR>\n" );
document.write( "Distance traveled to the breakdown: 1 * s = s miles<BR>\n" );
document.write( "(d-s) = distance traveled at .75s<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d-s%29%2F%28.75s%29 ALIGN=MIDDLE  ALT=\"%28d-s%29%2F%28.75s%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = time at slower rate<BR>\n" );
document.write( "write a time equation<BR>\n" );
document.write( "1 + .5 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d-s%29%2F%28.75s%29 ALIGN=MIDDLE  ALT=\"%28d-s%29%2F%28.75s%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fs ALIGN=MIDDLE  ALT=\"d%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 2<BR>\n" );
document.write( "1.5 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d-s%29%2F%28.75s%29 ALIGN=MIDDLE  ALT=\"%28d-s%29%2F%28.75s%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fs ALIGN=MIDDLE  ALT=\"d%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d-s%29%2F%28.75s%29 ALIGN=MIDDLE  ALT=\"%28d-s%29%2F%28.75s%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fs ALIGN=MIDDLE  ALT=\"d%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 2 - 1.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d-s%29%2F%28.75s%29 ALIGN=MIDDLE  ALT=\"%28d-s%29%2F%28.75s%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fs ALIGN=MIDDLE  ALT=\"d%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + .5<BR>\n" );
document.write( "multiply by .75s to clear the denominators<BR>\n" );
document.write( "d - s = .75d + .5(.75s)<BR>\n" );
document.write( "d - s = .75d + .375s<BR>\n" );
document.write( "d - .75d = .375s + s<BR>\n" );
document.write( ".25d = 1.375s<BR>\n" );
document.write( "multiply both sides by 4<BR>\n" );
document.write( "d = 5.5s<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"If the train had covered 75 miles more before the break down, it could be only 1 hour late.\"<BR>\n" );
document.write( "I made a big mistake here, instead \"75 mi more\" I used 75 mi, try to correct this now<BR>\n" );
document.write( ":<BR>\n" );
document.write( "write a time equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28s%2B75%29%29%2Fs ALIGN=MIDDLE  ALT=\"%28%28s%2B75%29%29%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + .5 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d-%28s%2B75%29%29%2F%28.75s%29 ALIGN=MIDDLE  ALT=\"%28d-%28s%2B75%29%29%2F%28.75s%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fs ALIGN=MIDDLE  ALT=\"d%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28s%2B75%29%29%2Fs ALIGN=MIDDLE  ALT=\"%28%28s%2B75%29%29%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d-%28s%2B75%29%29%2F%28.75s%29 ALIGN=MIDDLE  ALT=\"%28d-%28s%2B75%29%29%2F%28.75s%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fs ALIGN=MIDDLE  ALT=\"d%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 1 - .5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28s%2B75%29%29%2Fs ALIGN=MIDDLE  ALT=\"%28%28s%2B75%29%29%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d-%28s%2B75%29%29%2F%28.75s%29 ALIGN=MIDDLE  ALT=\"%28d-%28s%2B75%29%29%2F%28.75s%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fs ALIGN=MIDDLE  ALT=\"d%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + .5<BR>\n" );
document.write( "Multiply by .75s to clear the denominators<BR>\n" );
document.write( ".75(s+75) + (d-s-75) = .75d + .5(.75s)<BR>\n" );
document.write( ".75s + 56.25 + d - s - 75 = .75d = .375s<BR>\n" );
document.write( "Combine like terms<BR>\n" );
document.write( ".75s - s - .375s + d - .75d = 75 - 56.25<BR>\n" );
document.write( "-.625s + .25d = 18.75<BR>\n" );
document.write( "Replace d with 5.5s<BR>\n" );
document.write( "-.625s + .25(5.5s) = 18.75<BR>\n" );
document.write( "-.625s + 1.375s = 18.75<BR>\n" );
document.write( ".75s = 18.75<BR>\n" );
document.write( "s = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18.75%2F.75 ALIGN=MIDDLE  ALT=\"18.75%2F.75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = 25 mph is the initial speed of the train<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "See if this checks out, d = 5.5(25) = 137.5 mi and .75(25) = 18.75 mph<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2825%2B75%29%29%2F25 ALIGN=MIDDLE  ALT=\"%28%2825%2B75%29%29%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" > + .5 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28137.5-100%29%29%2F%2818.75%29 ALIGN=MIDDLE  ALT=\"%28137.5-100%29%29%2F%2818.75%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=137.5%2F25 ALIGN=MIDDLE  ALT=\"137.5%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2F25 ALIGN=MIDDLE  ALT=\"100%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=37.5%2F18.75 ALIGN=MIDDLE  ALT=\"37.5%2F18.75\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=137.5%2F25 ALIGN=MIDDLE  ALT=\"137.5%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" > + .5<BR>\n" );
document.write( "4 + 2 = 5.5 + .5; checks out \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );