document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174234>Question 174234</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am doing a practice test for a nursing entrance exam: If sally can paint a house in 4hrs, and john can paint the same house in 6hrs. How long will it take for both of them to paint the house together? <BR>\n" );
document.write( "H=4<BR>\n" );
document.write( "j=6     4+6=10  10/2=5 so 2hrs and 30min. the real answer is 2hrs and 24 min.\r<BR>\n" );
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document.write( "Please show me HOW TO FORMULATE my answer, because i am good at math, but this ? has me stumped by the answer. \r<BR>\n" );
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document.write( "A different problem, but the same type of ?: jim can fill a pool carrying buckets of water in 30min. sue can do the same job in 45 min. tony can do the same job in 1 1/2 hrs. how quickly can all 3 fill the pool together?<BR>\n" );
document.write( "j=30m<BR>\n" );
document.write( "s=45m<BR>\n" );
document.write( "t=90m    30+45+90=165    165/3=55 avg of min.   55/3=18.1...  so about 18min\r<BR>\n" );
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document.write( "                                ...but the real ans is 15min. again, could you please show me HOW TO GET THE ANSWER, and what is the formal name for this type of word problem, so i could look up further info about it on the web. thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #129161 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=129161\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's one approach to these types of problems:<BR>\n" );
document.write( "Find the \"rate\" at which each person can do the job.<BR>\n" );
document.write( "For the house-painting job, we'll find how much of the house can be painted by each participant in 1 hour.<BR>\n" );
document.write( "If Sally can paint the house in 4 hours, then she can paint 1/4 of the house in 1 hour.<BR>\n" );
document.write( "If John can paint the house in 6 hours, then he can paint 1/6 of the house in 1 hour. So, together, they can paint 1/4 + 1/6 = 5/12 of the house in 1 hour.<BR>\n" );
document.write( "If the two of them can paint 5/12 of the house in 1 hour, then it will take them 12/5 hours to paint the house.<BR>\n" );
document.write( "12/5 = 2 2/5 hours = 2 hours and 24 minutes.<BR>\n" );
document.write( "Similarly for the second problem, find the \"rate\" at which each person can fill the pool.<BR>\n" );
document.write( "Jim can fill the pool in 30 minutes, so he can fill 1/30 of the pool in 1 minute.<BR>\n" );
document.write( "Sue can fill the pool in 45 minutes, so she can fill 1/45 of the pool in 1 minute.<BR>\n" );
document.write( "Tony can fill the pool in 90 minutes (1 1/2 hrs), so he can fill 1/90 of the pool in 1 minute.<BR>\n" );
document.write( "Working together, they can fill (1/30 + 1/45 + 1/90 = 6/90 = 1/15) of the pool in 1 minute, so it would take them 15/1 = 15 minutes to fill the pool together.<BR>\n" );
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