document.write( "Question 1032869: Lala can remove the engine from a car in 4 hours. George can do it in 3 hours. George starts the job alone. One hour later, Lala begins helping him. How long will Lala work before the engine is out? \n" ); document.write( "

Algebra.Com's Answer #647668 by josmiceli(19441) $\"\"$ $\"About$

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George's rate of working: [ 1 engine removed ] / [ 3 hrs ]
\n" ); document.write( "In 1 hr, the fraction of the job that George gets done is:
\n" ); document.write( " $\"+1%2A%28+1%2F3%29+=+1%2F3+\"$
\n" ); document.write( "That means 2/3 of the job is left to do
\n" ); document.write( "-----------------------
\n" ); document.write( "Lala's rate of working: [ 1 engine removed ] / [ 4 hrs ]
\n" ); document.write( "Now they work together to do the remaining 2/3 of the job
\n" ); document.write( "Let $\"+t+\"$ = their time in hrs to finish the job
\n" ); document.write( "Add their rates of working:
\n" ); document.write( " $\"+1%2F3+%2B+1%2F4+=+%28%282%2F3%29%29+%2F+t+\"$
\n" ); document.write( " $\"+1%2F3+%2B+1%2F4+=+2%2F%283t%29+\"$
\n" ); document.write( "Multiply both sides by $\"+12t+\"$
\n" ); document.write( " $\"+4t+%2B+3t+=+8+\"$
\n" ); document.write( " $\"+7t+=+8+\"$
\n" ); document.write( " $\"+t+=+8%2F7+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+%281%2F7%29%2A60+=+8.57+\"$
\n" ); document.write( " $\"+.57%2A60+=+34+\"$
\n" ); document.write( "Lala will work 1 hr 8 min 34 sec before engine is out
\n" ); document.write( "--------------------------
\n" ); document.write( "check:
\n" ); document.write( " $\"+1%2F3+%2B+1%2F4+=+2%2F%283t%29+\"$
\n" ); document.write( " $\"+1%2F3+%2B+1%2F4+=+2%2F%283%2A1.143%29+\"$
\n" ); document.write( " $\"+.333+%2B+.25+=+2%2F3.429+\"$
\n" ); document.write( " $\"+.583+=+.583+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );