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 #754986 by VFBundy(438)\"\" \"About 
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Rate larger unit takes to melt iron: 1/x per hour
\n" ); document.write( "Rate smaller unit takes to melt iron: 1/(x+40) per hour
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\n" ); document.write( "Rate of both working together: 1/x + 1/(x+40) = 1/15 per hour
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\n" ); document.write( "Solve for x:
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\n" ); document.write( "\"1%2Fx+%2B+1%2F%28x%2B40%29+=+1%2F15\"
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\n" ); document.write( "\"%28x%2B40%29%2Fx%28x%2B40%29+%2B+x%2Fx%28x%2B40%29+=+1%2F15\"
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\n" ); document.write( "\"%28%28x%2B40%29%2Bx%29%2Fx%28x%2B40%29+=+1%2F15\"
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\n" ); document.write( "\"%282x%2B40%29%2Fx%28x%2B40%29+=+1%2F15\"
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\n" ); document.write( "\"15%282x%2B40%29+=+x%28x%2B40%29\"
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\n" ); document.write( "\"30x+%2B+600+=+x%5E2+%2B40x\"
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\n" ); document.write( "\"x%5E2+%2B+10x+-+600+=+0\"
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\n" ); document.write( "\"%28x-20%29%28x%2B30%29+=+0\"
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\n" ); document.write( "x = 20 and x = -30
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\n" ); document.write( "Since the rate cannot be a negative number, we can ignore x = -30. So, the final answer is x = 20.
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\n" ); document.write( "Rate larger unit takes to melt iron: 1/x per hour = 1/20 per hour
\n" ); document.write( "Rate smaller unit takes to melt iron: 1/(x+40) per hour = 1/60 per hour
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\n" ); document.write( "So, working alone, the larger unit takes 20 hours to melt the iron and the smaller unit takes 60 hours. \n" ); document.write( "
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