document.write( "Question 1137144: A small heating unit takes 40 h longer to melt a piece of iron than does a larger unit. Working together, the heating units can melt the iron in 15 h. How long would it take each heating unit, working alone, to melt the iron?
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Algebra.Com's Answer #754985 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+t+\"$ = time in hrs for the larger unit
\n" ); document.write( " $\"+t+%2B+40+\"$ = time in hrs for the smaller unit
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\n" ); document.write( "Add their rates of melting to get their rate melting together
\n" ); document.write( " $\"+1%2Ft+%2B+1%2F%28+t+%2B+40+%29+=+1%2F15+\"$
\n" ); document.write( "Multiply both sides by $\"+t%2A%28+t+%2B+40+%29%2A15+\"$
\n" ); document.write( " $\"+15%2A%28+t+%2B+40+%29+%2B+15t+=+t%2A%28+t++%2B+40+%29+\"$
\n" ); document.write( " $\"+15t+%2B+600+%2B+15t+=+t%5E2+%2B+40t+\"$
\n" ); document.write( " $\"+t%5E2+%2B+10t+-+600+=+0+\"$
\n" ); document.write( " $\"+%28+t+%2B+30+%29%2A%28+t+-+20+%29+\"$
\n" ); document.write( " $\"+t+=+20+\"$ ( can't use negative result )
\n" ); document.write( "and
\n" ); document.write( " $\"+t+%2B+40+=+60+\"$
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\n" ); document.write( "Larger unit takes 20 hrs
\n" ); document.write( "Smaller unit takes 60 hrs
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\n" ); document.write( "check:
\n" ); document.write( " $\"+1%2F20+%2B+1%2F60+=+1%2F15+\"$
\n" ); document.write( " $\"+.05+%2B+.01667+=+.06667+\"$
\n" ); document.write( " $\"+.06667+=+.06667+\"$
\n" ); document.write( "OK
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