document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=323259>Question 323259</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you please help me figure out the answer to this word problem?\r<BR>\n" );
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document.write( "If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together?\r<BR>\n" );
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document.write( "A. 2 hrs and 24 mins<BR>\n" );
document.write( "B. 3 hours and 12 mins<BR>\n" );
document.write( "C. 3 hours and 44 mins<BR>\n" );
document.write( "D. 4 hours and 10mins<BR>\n" );
document.write( "E. 4 hours and 33 mins.\r<BR>\n" );
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document.write( "I thought that the way to get the answer would be to add both times together (4+6=10) and divide by two (the number of people painting), to get 5hrs as the answer. Apparently this is not correct, since 5 hrs is not one of the answers.<BR>\n" );
document.write( "Thanks for helping.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #231395 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=231395\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"If Sally can paint a house in 4 hours\", then she can paint <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;\" > of the house in 1 hour (divide each number by 4). So Sally's 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;\" > of a house per hour. Likewise, since \"John can paint the same house in 6 hours\", he can paint <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the house in one hour. So his rate is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > of a house per hour.\r<BR>\n" );
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document.write( "Now add the two rates to get: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4%2B1%2F6=3%2F12%2B2%2F12=5%2F12 ALIGN=MIDDLE  ALT=\"1%2F4%2B1%2F6=3%2F12%2B2%2F12=5%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So their combined rate (if conditions are perfect) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F12 ALIGN=MIDDLE  ALT=\"5%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > houses per hour. In other words, together they can paint <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F12 ALIGN=MIDDLE  ALT=\"5%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the house in one hour.\r<BR>\n" );
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document.write( "Now let 't' be the time that it takes them to complete the task. If we multiply the rate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F12 ALIGN=MIDDLE  ALT=\"5%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > by the time 't', we will get a complete job. This is simply denoted by 1 (since we want to paint <u>one</u> house).\r<BR>\n" );
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document.write( "Basically, we then get the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F12%29t=1 ALIGN=MIDDLE  ALT=\"%285%2F12%29t=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F12%29t=1 ALIGN=MIDDLE  ALT=\"%285%2F12%29t=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%2812%29%285%2Fcross%2812%29%29t=1%2A12 ALIGN=MIDDLE  ALT=\"cross%2812%29%285%2Fcross%2812%29%29t=1%2A12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 12.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5t=12 ALIGN=MIDDLE  ALT=\"5t=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply and simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%285%29t%29%2Fcross%285%29=12%2F5 ALIGN=MIDDLE  ALT=\"%28cross%285%29t%29%2Fcross%285%29=12%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 5.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=12%2F5 ALIGN=MIDDLE  ALT=\"t=12%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "So working together, they can paint 1 house in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=12%2F5 ALIGN=MIDDLE  ALT=\"t=12%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours. Convert it to a mixed fraction to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F5=2%262%2F5 ALIGN=MIDDLE  ALT=\"12%2F5=2%262%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Finally, multiply <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;\" > by 60 (to convert it into minutes) to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%282%2F5%29=120%2F5=24 ALIGN=MIDDLE  ALT=\"60%282%2F5%29=120%2F5=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F5 ALIGN=MIDDLE  ALT=\"12%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%262%2F5 ALIGN=MIDDLE  ALT=\"2%262%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours is 2 hours and 24 minutes.\r<BR>\n" );
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document.write( "So they can paint the house in 2 hours and 24 minutes. This means that the answer is A. 2 hrs and 24 mins </SPAN>\n" );
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