document.write( "Question 1057934: Sofia can type the work in 10 hours. Noga can do it in 15 hours. They work together for 4 hours. Then Sofia left and Noga finished the job. How long did it take \n" ); document.write( "

Algebra.Com's Answer #672936 by josmiceli(19441) $\"\"$ $\"About$

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Add their rates of working to get
\n" ); document.write( "their rate working together
\n" ); document.write( "Sofia's rate:
\n" ); document.write( "[ 1 job ] / [ 10 hrs ]
\n" ); document.write( "Noga's rate:
\n" ); document.write( "[ 1 job ] / [ 15 hrs ]
\n" ); document.write( "---------------------
\n" ); document.write( "Let $\"+x+\"$ = the fraction of the job they
\n" ); document.write( "get done in 4 hrs
\n" ); document.write( " $\"+1%2F10+%2B+1%2F15+=+x%2F4+\"$
\n" ); document.write( "Multiply both sides by $\"+60+\"$
\n" ); document.write( " $\"+6+%2B+4+=+15x+\"$
\n" ); document.write( " $\"+15x+=+10+\"$
\n" ); document.write( " $\"+x+=+2%2F3+\"$
\n" ); document.write( "----------------------
\n" ); document.write( "2/3 of the job got done, so 1/3 is left
\n" ); document.write( "Noga finished the job.
\n" ); document.write( "Let $\"+t+\"$ = time in hrs for her to finish
\n" ); document.write( " $\"+1%2F15+=+%28%281%2F3%29%29+%2F+t+\"$
\n" ); document.write( " $\"+1%2F15+=+1%2F%28%283t%29%29+\"$
\n" ); document.write( "Multiply both sides by $\"+15t+\"$
\n" ); document.write( " $\"+t+=+5+\"$
\n" ); document.write( "-----------------
\n" ); document.write( " $\"+4+%2B+5+=+9+\"$
\n" ); document.write( "The job took 9 hrs \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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