document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206862>Question 1206862</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In 8 minutes, a conveyor belt can move 1,000 bushels of corn into a storage bin. A smaller belt can move 1,000 bushels to the storage bin in 14 minutes. If both belts are used, how long will it take to move 1,000 bushels to the storage bin? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844550 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=844550\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "If this problem is on a competitive timed test, then you can use the standard shortcut for solving problems like this involving two workers: If the times for the two workers to perform the job individually are A and B, then the time required for them to do the job together is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28A%2AB%29%2F%28A%2BB%29 ALIGN=MIDDLE  ALT=\"%28A%2AB%29%2F%28A%2BB%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "For this problem: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2814%2A8%29%2F%2814%2B8%29=112%2F22=56%2F11 ALIGN=MIDDLE  ALT=\"%2814%2A8%29%2F%2814%2B8%29=112%2F22=56%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: 56/11 hours, or 5 1/11 hours<br><BR>\n" );
document.write( "If this problem is on a test in a classroom where you are supposed to show a formal algebraic solution, then the solution might look something like this.<br><BR>\n" );
document.write( "Let x be the number of hours it takes the two of them together to do the job.<br><BR>\n" );
document.write( "1/8 = fraction of job the first belt does in 1 minute<BR>\n" );
document.write( "1/14 = fraction of job the second belt does in 1 minute<BR>\n" );
document.write( "1/x = fraction of job the two belts together do in 1 minute<br><BR>\n" );
document.write( "The fraction of the job they do together is the sum of the fractions of the job each does alone in 1 minute:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F8%2B1%2F14=1%2Fx ALIGN=MIDDLE  ALT=\"1%2F8%2B1%2F14=1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Multiply the equation by the least common multiple of the denominators, which is 56x:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%2B4x=56 ALIGN=MIDDLE  ALT=\"7x%2B4x=56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11x=56 ALIGN=MIDDLE  ALT=\"11x=56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=56%2F11 ALIGN=MIDDLE  ALT=\"x=56%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "And here is a different formal method for solving the problem and any similar problem.<br><BR>\n" );
document.write( "8 times 14 is 112.<br><BR>\n" );
document.write( "In 112 minutes, the first belt could do the job 112/8 = 14 times; in 112 minutes the second belt could do the job 112/14 = 8 times.  So together in 112 minutes the two could do the job 14+8 = 22 times.<br><BR>\n" );
document.write( "And so the number of minutes it will take the two belts together to do the one job is 112/22 = 56/11 = 5 1/11.<br><BR>\n" );
document.write( " </SPAN>\n" );
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