document.write( "Question 179308This question is from textbook
\n" ); document.write( ": Time off for lunch. It usually takes Eva 3 hours longer to
\n" ); document.write( "do the monthly payroll than it takes Cicely. They start
\n" ); document.write( "working on it together at 9:00 A.M. and at 5:00 P.M. they
\n" ); document.write( "have 90% of it done. If Eva took a 2-hour lunch break
\n" ); document.write( "while Cicely had none, then how much longer will it
\n" ); document.write( "take for them to finish the payroll working together? \n" ); document.write( "
Algebra.Com's Answer #134229 by josmiceli(19441)\"\" \"About 
You can put this solution on YOUR website!
Let \"t\"= the time it takes
\n" ); document.write( "Cicely to do monthly payroll
\n" ); document.write( "Then \"t+%2B+3\" will be the time it takes
\n" ); document.write( "Eva to do the payroll
\n" ); document.write( "Let \"c\"= the fraction of the 90% they
\n" ); document.write( "did working together
\n" ); document.write( "Let \"d\"= the fraction of the 90% Cicely
\n" ); document.write( "did working 2 hrs by herself
\n" ); document.write( "given:
\n" ); document.write( "Between 9AM and 5 PM, there are 8 hrs
\n" ); document.write( "If Eva took a 2-hour lunch break, then she only
\n" ); document.write( "worked 6 hrs on the payroll.
\n" ); document.write( "They actually worked together for 6 hrs
\n" ); document.write( "and Cicely worked alone for 2 hrs.
\n" ); document.write( "---------------------------------
\n" ); document.write( "Working together:
\n" ); document.write( "(1) \"1%2Ft+%2B+1%2F%28t%2B3%29+=+c%2F6\"
\n" ); document.write( "(2) \"1%2Ft+=+d%2F2\"
\n" ); document.write( "\"t+=+2%2Fd\"
\n" ); document.write( "\"t+%2B+3+=+%282%2Fb%29+%2B3\"
\n" ); document.write( "(3) \"c+%2B+d+=+.9\"
\n" ); document.write( "\"d+=+.9+-+a\"
\n" ); document.write( "--------------------
\n" ); document.write( "(1) \"1%2Ft+%2B+1%2F%28t%2B3%29+=+c%2F6\"
\n" ); document.write( "\"d%2F2+%2B+1%2F%28%282%2Fd%29+%2B+3%29+=+%28.9+-+d%29%2F6\"
\n" ); document.write( "\"d%2F2+%2B+1%2F%28%282+%2B+3d%29%2Fd%29+=+%28.9+-+d%29%2F6\"
\n" ); document.write( "\"d%2F2+%2B+d%2F%282+%2B+3d%29+=+%28.9+-+d%29%2F6\"
\n" ); document.write( "Multiply both sides by \"6%2A%282+%2B+3d%29\"
\n" ); document.write( "\"3d%2A%282+%2B+3d%29+%2B+6d+=+%282+%2B+3d%29%28.9+-+d%29\"
\n" ); document.write( "\"6d+%2B+9d%5E2+%2B+6d+=+1.8+%2B+2.7d+-+2d+-+3d%5E2\"
\n" ); document.write( "\"9d%5E2+%2B+12d+=+-3d%5E2+%2B+.7d+%2B+1.8\"
\n" ); document.write( "\"12d%5E2+%2B+11.3d+-+1.8+=+0\"
\n" ); document.write( "Solve using quadratic formula
\n" ); document.write( "\"d+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( "\"a+=+12\"
\n" ); document.write( "\"b+=+11.3\"
\n" ); document.write( "\"c+=+-1.8\"
\n" ); document.write( "\"d+=+%28-11.3+%2B-+sqrt%28+11.3%5E2-4%2A12%2A%28-1.8%29+%29%29%2F%282%2A12%29+\"
\n" ); document.write( "\"d+=+%28-11.3+%2B-+sqrt%28+127.69+%2B+86.4+%29%29%2F24+\"
\n" ); document.write( "\"d+=+%28-11.3+%2B-+sqrt%28+214.09+%29%29%2F24+\"
\n" ); document.write( "\"d+=+%28-11.3+%2B-+14.63%29%2F24+\"
\n" ); document.write( "\"d+=+%28-11.3+%2B+14.63%29%2F24\"
\n" ); document.write( "\"d+=+3.33%2F24\"
\n" ); document.write( "\"d+=+.139\"
\n" ); document.write( "And,since
\n" ); document.write( "(3) \"c+%2B+d+=+.9\"
\n" ); document.write( "\"c+%2B+.139+=+.9\"
\n" ); document.write( "\"c+=+.761\"
\n" ); document.write( "Also,since
\n" ); document.write( "\"t+=+2%2Fd\"
\n" ); document.write( "\"t+=+2%2F.139\"
\n" ); document.write( "\"t+=+14.39\"
\n" ); document.write( "Now I can solve for completing
\n" ); document.write( "the remaining 10% of the job
\n" ); document.write( "(1) \"1%2Ft+%2B+1%2F%28t%2B3%29+=+.1%2Ft%5Bx%5D\"
\n" ); document.write( "\"1%2F14.39+%2B+1%2F17.39+=+.1%2Ft%5Bx%5D\"
\n" ); document.write( "Multiply both sides by \"14.39%2A17.39%2At%5Bx%5D\"
\n" ); document.write( "\"17.39t%5Bx%5D+%2B+14.39t%5Bx%5D+=+.1%2A14.39%2A17.39\"
\n" ); document.write( "\"31.78t%5Bx%5D+=+25.024\"
\n" ); document.write( "\"t%5Bx%5D+=+.787\"hr
\n" ); document.write( "\".787%2A60+=+47.25\"
\n" ); document.write( "Working together, they can finish the job in 47.25 min
\n" ); document.write( "check:
\n" ); document.write( "(1) \"1%2Ft+%2B+1%2F%28t%2B3%29+=+c%2F6\"
\n" ); document.write( "\"1%2F14.39+%2B+1%2F17.39+=+.761%2F6\"
\n" ); document.write( "\".0695+%2B+.0575+=+.1268\"
\n" ); document.write( "\".127+=+.1268\" close
\n" ); document.write( "(2) \"1%2Ft+=+d%2F2\"
\n" ); document.write( "\"1%2F14.39+=+.139%2F2\"
\n" ); document.write( "\".0695+=+.0695\" OK
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