document.write( "Question 783511: With the old combine, Nikita's entire wheat crop can be harvested in 72 hours, but a new combine can do the same job in 48 hours. How many hours would it take to harvest the crop with both combines operating? \r
\n" ); document.write( "\n" ); document.write( "Hint: The rate for the old combine is 1/72 crop/hour and for the new one it is 1/48 crop/hour. Together the rate is 1/x crop/hour \n" ); document.write( "

Algebra.Com's Answer #476823 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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With the old combine, Nikita's entire wheat crop can be harvested in 72 hours, but a new combine can do the same job in 48 hours.
\n" ); document.write( " How many hours would it take to harvest the crop with both combines operating?
\n" ); document.write( ":
\n" ); document.write( "An easy way to do this:
\n" ); document.write( "let t = time when the two combines work together
\n" ); document.write( "Let the completed job = 1
\n" ); document.write( "Each combine does a fraction of the job, the two fractions add up to 1
\n" ); document.write( " $\"t%2F72\"$ + $\"t%2F48\"$ = 1
\n" ); document.write( "least common multiple of these two denominators, 144
\n" ); document.write( "144* $\"t%2F72\"$ + 144* $\"t%2F48\"$ = 144*1
\n" ); document.write( "Cancel the denominators, resulting in
\n" ); document.write( "2t + 3t = 144
\n" ); document.write( "5t = 144
\n" ); document.write( "t = 144/5
\n" ); document.write( "t = 28.8 hr working together
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check this on your calc, enter
\n" ); document.write( " $\"28.8%2F72\"$ + $\"28.8%2F48\"$ = \n" ); document.write( "

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