document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=403408>Question 403408</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If Mike takes 3 hours to make one bicycle and Henry takes 4 hours to make one bicycle, how many hours will it take them to make 7 bicycles together?  (I CANNOT set this up correctly, and would appreciate any advice you would share. Thanks for your time.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #285261 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=285261\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First figure out how long it takes them to make ONE bicycle. If you get stuck with problems like this, always remember that you must start with one (if you want to get to 7)\r<BR>\n" );
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document.write( "Since \"Mike takes 3 hours to make one bicycle\", we know that his rate is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > bikes an hour. In other words, in one hour, he has one-third of a bike done.\r<BR>\n" );
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document.write( "Also, we know that \"Henry takes 4 hours to make one bicycle\", so by similar logic his rate is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > bikes per hour\r<BR>\n" );
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document.write( "Now add their two rates. This is of course assuming ideal conditions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3%2B1%2F4=4%2F12%2B3%2F12=%284%2B3%29%2F12=7%2F12 ALIGN=MIDDLE  ALT=\"1%2F3%2B1%2F4=4%2F12%2B3%2F12=%284%2B3%29%2F12=7%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So under perfect conditions (ie there's no overlap between the two workers, they're working consistently, etc) their combined rate is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F12 ALIGN=MIDDLE  ALT=\"7%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > bikes an hour. Stated another way, in one hour, together they've completed <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F12 ALIGN=MIDDLE  ALT=\"7%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > of a single bike.\r<BR>\n" );
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document.write( "But we want a WHOLE bike, not <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F12 ALIGN=MIDDLE  ALT=\"7%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > of a bike. So we WANT to obtain the value 1. How do we this? We just let some time pass of course. If we let the two workers keep working, they'll get 1 bike done eventually (no matter how slow they go)\r<BR>\n" );
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document.write( "So let's let some unknown time pass. We'll call this time 't'. If t = 1, then 1 hour passes and they've completed <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F12 ALIGN=MIDDLE  ALT=\"7%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > of a single bike. Now say 2 hours pass, which means t = 2 now. So this means they've completed ANOTHER <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F12 ALIGN=MIDDLE  ALT=\"7%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > of that same bike. Now add the fractions to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F12%2B7%2F12=14%2F12=1%262%2F12 ALIGN=MIDDLE  ALT=\"7%2F12%2B7%2F12=14%2F12=1%262%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice how <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%262%2F12 ALIGN=MIDDLE  ALT=\"1%262%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > is clearly over 1. So the two workers have completed bike #1 and have moved onto bike #2 in two hours. So we know for sure that the first bike took under 2 hours to make.\r<BR>\n" );
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document.write( "In general, given 't' hours, the two workers will make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=expr%287%2F12%29t ALIGN=MIDDLE  ALT=\"expr%287%2F12%29t\"   DISABLED_style= \"max-width:90%; height:auto;\" > bikes. We just don't know 't' (yet)\r<BR>\n" );
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document.write( "Since we're forcing the number of bikes to be 1, this means that we're setting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=expr%287%2F12%29t ALIGN=MIDDLE  ALT=\"expr%287%2F12%29t\"   DISABLED_style= \"max-width:90%; height:auto;\" > equal to 1 to get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=expr%287%2F12%29t=1 ALIGN=MIDDLE  ALT=\"expr%287%2F12%29t=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which is the equation we want to solve.\r<BR>\n" );
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document.write( "To do that, multiply both sides by 12 and then divide both sides by 7 to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=12%2F7 ALIGN=MIDDLE  ALT=\"t=12%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > (note: you can just flip <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F12 ALIGN=MIDDLE  ALT=\"7%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F7 ALIGN=MIDDLE  ALT=\"12%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Note: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F7=1%265%2F7 ALIGN=MIDDLE  ALT=\"12%2F7=1%265%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So it takes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F7 ALIGN=MIDDLE  ALT=\"12%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%265%2F7 ALIGN=MIDDLE  ALT=\"1%265%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours to make ONE bike...phew. With me so far?\r<BR>\n" );
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document.write( "If not, then go back over all of the above (and ask me about anything before moving on)\r<BR>\n" );
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document.write( "Since we want 7 bikes, we can just scale up (again assuming everything stays the same). So just multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F7 ALIGN=MIDDLE  ALT=\"12%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > by 7 to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2F7%29%287%29=%2812%2F7%29%2A%287%2F1%29=%2812%2A7%29%2F%287%2A1%29=84%2F7=12 ALIGN=MIDDLE  ALT=\"%2812%2F7%29%287%29=%2812%2F7%29%2A%287%2F1%29=%2812%2A7%29%2F%287%2A1%29=84%2F7=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So it will take 12 hours to make 7 bikes. Note: the book most likely chose these numbers to make the answer clean.\r<BR>\n" );
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