document.write( "Question 982505: Aira can do a job in 4 hours and Queenie can do the same in 9 hours. They start working together. After 2 hours, Queenie leaves and Aira finishes the job alone. How many hours did Aira take to finish the job alone? \n" ); document.write( "

Algebra.Com's Answer #603328 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+x+\"$ = the fraction of the job they
\n" ); document.write( "do working together for 2 hrs
\n" ); document.write( "Aira's rate of working is:
\n" ); document.write( "[ 1 job done / 4 hrs ]
\n" ); document.write( "Queenie's rate of working is:
\n" ); document.write( "[ 1 job done / 9 hrs ]
\n" ); document.write( "----------------------------
\n" ); document.write( "Add their rates of working to get
\n" ); document.write( "their rate working together
\n" ); document.write( "Their rate working together is: $\"+x%2F2+\"$
\n" ); document.write( " $\"+1%2F4+%2B+1%2F9+=+x%2F2+\"$
\n" ); document.write( "Multiply both sides by $\"+36+\"$
\n" ); document.write( " $\"+9+%2B+4+=+18x+\"$
\n" ); document.write( " $\"+18x+=+13+\"$
\n" ); document.write( " $\"+x+=+13%2F18+\"$
\n" ); document.write( "In 2 hrs, they do $\"+13%2F18+\"$ of the work. That
\n" ); document.write( "means there is $\"+1+-+13%2F81+=+5%2F18+\"$
\n" ); document.write( "of the work left to do
\n" ); document.write( "-------------------------
\n" ); document.write( "Let $\"+t+\"$ = time in hrs for Aira to
\n" ); document.write( "finish the job
\n" ); document.write( " $\"+1%2F4+=+%28%28+5%2F18+%29%29+%2F+t+\"$
\n" ); document.write( " $\"+1%2F4+=+5%2F%2818t%29+\"$
\n" ); document.write( "Multiply both sides by $\"+36t+\"$
\n" ); document.write( " $\"+9t+=+10+\"$
\n" ); document.write( " $\"+t+=+10%2F9+=+1+%2B+1%2F9+\"$
\n" ); document.write( " $\"+%28+1%2F9+%29%2A60+=+6+%2B+2%2F3+\"$
\n" ); document.write( " $\"+%28+2%2F3%29%2A60+=+40+\"$
\n" ); document.write( "---------------------
\n" ); document.write( "Aira finishes the job in 1 hr 6 min 40 sec
\n" ); document.write( "check answer:
\n" ); document.write( " $\"+1%2F4+=+%28%28+5%2F18+%29%29+%2F+t+\"$
\n" ); document.write( " $\"+1%2F4+=+%28%28+5%2F18+%29%29+%2F+%28%28+10%2F9+%29%29+\"$
\n" ); document.write( " $\"+1%2F4+=+%28+5%2F18+%29%2A%28+9%2F10+%29+\"$
\n" ); document.write( " $\"+1%2F4+=+%28+5%2F10+%29%2A%28+9%2F18+%29+\"$
\n" ); document.write( " $\"+1%2F4+=+%28+1%2F2+%29%2A%28+1%2F2+%29+\"$
\n" ); document.write( " $\"+1%2F4+=+1%2F4+\"$
\n" ); document.write( "OK
\n" ); document.write( "Hope I got it!\r
\n" ); document.write( "\n" ); document.write( " \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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