document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190679>Question 1190679</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bakery owner hires a new assistant to decorate doughnuts. The owner can decorate the day's supply four times as quickly as the assistant. Working together, they can decorate all the doughnuts in 32 minutes. How long would it take each to decorate the doughnuts, working individually? </SPAN>\n" );
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document.write( "The owner works 4 times as fast as his assistant, so when working together he does 4/5 of the work.<br><BR>\n" );
document.write( "Working together, they take 32 minutes to do the job.<br><BR>\n" );
document.write( "So the owner does 4/5 of the job in 32 minutes and the assistant does 1/5.<br><BR>\n" );
document.write( "The owner does 4/5 of the job in 32 minutes, so the number of minutes it would take him to do the job alone is 32/(4/5) = 32*(5/4) = 40.<br><BR>\n" );
document.write( "The assistant does 1/5 of the job in 32 minutes, so the number of minutes it would take him to do the job alone is 32*5=160.<br><BR>\n" );
document.write( "ANSWERS:<BR>\n" );
document.write( "owner 40 minutes<BR>\n" );
document.write( "assistant 160 minutes<br><BR>\n" );
document.write( "Formally...<br><BR>\n" );
document.write( "x = minutes the owner takes to do the job<BR>\n" );
document.write( "4x = minutes the assistant takes to do the job<BR>\n" );
document.write( "32 = minutes it takes them together to do the job<BR>\n" );
document.write( "1/x = fraction of the job the owner does in 1 minute<BR>\n" );
document.write( "1/(4x) = fraction the assistant does in 1 minute<BR>\n" );
document.write( "1/32 = fraction they do together in 1 minute<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx%2B1%2F%284x%29=1%2F32 ALIGN=MIDDLE  ALT=\"1%2Fx%2B1%2F%284x%29=1%2F32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "multiply by 32x to clear fractions:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32%2B8=x ALIGN=MIDDLE  ALT=\"32%2B8=x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=40 ALIGN=MIDDLE  ALT=\"x=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWERS:<BR>\n" );
document.write( "time for owner to do the job alone: x = 40 minutes<BR>\n" );
document.write( "time for assistant to do the job alone: 4x = 160 minutes<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );