document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73619>Question 73619</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If Steven can mix 20 drinks in 5 mins., Sue can mix 20 drinks in 10 mins., and Jack can mix 20 drinks in 15 mins, how much time will it take all 3 of them working together to mix the 20 drinks? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52648 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=52648\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Steven mixes 20 drinks in 5 minutes.  Therefore, he mixes 4 drinks per minute. (Get this by<BR>\n" );
document.write( "dividing 5 into 20.)<BR>\n" );
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document.write( "Sue mixes 20 drinks in 10 minutes.  Therefore, she mixes 2 drinks per minute.<BR>\n" );
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document.write( "Jack mixes 20 drinks in 15 minutes.  Therefore, he mixes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F15+=+4%2F3 ALIGN=MIDDLE  ALT=\"20%2F15+=+4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > drinks per minute.<BR>\n" );
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document.write( "The problem implies that they all start mixing drinks at the same time.  Therefore in mixing<BR>\n" );
document.write( "drinks they all work the same time t.  And we need to know when they reach 20 drinks total.<BR>\n" );
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document.write( "In equation form we multiply their individual mixing rates by the time t to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2At+%2B+2%2At+%2B+%284%2F3%29%2At+=+20 ALIGN=MIDDLE  ALT=\"4%2At+%2B+2%2At+%2B+%284%2F3%29%2At+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Factor the t out on the left side:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%284+%2B+2+%2B%284%2F3%29%29%2At+=+20 ALIGN=MIDDLE  ALT=\"+%284+%2B+2+%2B%284%2F3%29%29%2At+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Putting all the numbers in the parentheses over the common denominator of 3 results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2812%2F3%29%2B+%286%2F3%29+%2B+%284%2F3%29%29%2At+=+20 ALIGN=MIDDLE  ALT=\"%28%2812%2F3%29%2B+%286%2F3%29+%2B+%284%2F3%29%29%2At+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Combine all the fractions by adding their numerators and placing them over the common<BR>\n" );
document.write( "denominator of 3 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2822%2F3%29%2At+=+20 ALIGN=MIDDLE  ALT=\"%2822%2F3%29%2At+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve this problem by dividing both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22%2F3 ALIGN=MIDDLE  ALT=\"22%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. On the left side this just leaves<BR>\n" );
document.write( "t. On the right side, recall the rule that dividing by a fraction is the same as multiplying<BR>\n" );
document.write( "by its inverse.  Therefore, the right side can be determined by multiplying:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20+%2A+%283%2F22%29+=+%2860%2F22%29+=+%2830%2F11%29 ALIGN=MIDDLE  ALT=\"20+%2A+%283%2F22%29+=+%2860%2F22%29+=+%2830%2F11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Take your calculator and divide 30 by ll to find that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2F11+=+2.727 ALIGN=MIDDLE  ALT=\"30%2F11+=+2.727\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the answer<BR>\n" );
document.write( "is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+2.727 ALIGN=MIDDLE  ALT=\"t+=+2.727\"   DISABLED_style= \"max-width:90%; height:auto;\" >minutes. And 0.727 times 60 seconds is about 43.6 seconds. So the answer to<BR>\n" );
document.write( "this problem is t = 2 minutes and 43.6 seconds.<BR>\n" );
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document.write( "Hope this helps you to think your way through the problem.<BR>\n" );
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