document.write( "Question 921634: Three machines A,B,C operating at the same time can do a job in 8 hours. If A alone operates for 2 hours and B alone for 3 hours, one-fourth of the job is done. Now if B alone operates for 5 hours and C alone for 14 hours, one-half of the job is done. How many hours would it take each to do the job alone?\r
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Algebra.Com's Answer #559225 by ankor@dixie-net.com(22740)\"\" \"About 
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Three machines A,B,C operating at the same time can do a job in 8 hours.
\n" ); document.write( " If A alone operates for 2 hours and B alone for 3 hours, one-fourth of the job is done.
\n" ); document.write( " Now if B alone operates for 5 hours and C alone for 14 hours, one-half of the job is done.
\n" ); document.write( " How many hours would it take each to do the job alone?
\n" ); document.write( ":
\n" ); document.write( "let a = time required by machine A alone
\n" ); document.write( "let b = time required by B
\n" ); document.write( "let c = time required by C
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\n" ); document.write( "Write an equation for each statement.
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\n" ); document.write( "let the completed job = 1
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\n" ); document.write( "Three machines A,B,C operating at the same time can do a job in 8 hours.
\n" ); document.write( "\"8%2Fa\" + \"8%2Fb\" + \"8%2Fc\" = 1
\n" ); document.write( ":
\n" ); document.write( "If A alone operates for 2 hours and B alone for 3 hours, one-fourth of the job is done.
\n" ); document.write( "\"2%2Fa\" + \"3%2Fb\" = \"1%2F4\"
\n" ); document.write( ":
\n" ); document.write( " Now if B alone operates for 5 hours and C alone for 14 hours, one-half of the job is done.
\n" ); document.write( "\"5%2Fb\" + \"14%2Fc\" = \"1%2F2\"
\n" ); document.write( ":
\n" ); document.write( "multiply the 2nd equation by 4, subtract from the 1st equation
\n" ); document.write( "\"8%2Fa\" + \"8%2Fb\" + \"8%2Fc\" = 1
\n" ); document.write( "\"8%2Fa\" + \"12%2Fb\" + 0 = 1
\n" ); document.write( "---------------------------------subtraction eliminates a
\n" ); document.write( "0 - \"4%2Fb\" + \"8%2Fc\" = 0
\n" ); document.write( "\"8%2Fc\" = \"4%2Fb\"
\n" ); document.write( "divide both sides 4
\n" ); document.write( "\"2%2Fc\" = \"1%2Fb\"
\n" ); document.write( "cross multiply
\n" ); document.write( "1c = 2b
\n" ); document.write( "in the 3rd original equation replace c with 2b
\n" ); document.write( "\"5%2Fb\" + \"14%2F%282b%29\" = \"1%2F2\"
\n" ); document.write( "Reduce the fraction
\n" ); document.write( "\"5%2Fb\" + \"7%2Fb\" = \"1%2F2\"
\n" ); document.write( "\"12%2Fb\" = \"1%2F2\"
\n" ); document.write( "b = 24 hrs working alone
\n" ); document.write( "then
\n" ); document.write( "c = 2(24)
\n" ); document.write( "c = 48 hrs alone
\n" ); document.write( "In the 2nd original equation, replace b with 24
\n" ); document.write( "\"2%2Fa\" + \"3%2F24\" = \"1%2F4\"
\n" ); document.write( "reduce fraction
\n" ); document.write( "\"2%2Fa\" + \"1%2F8\" = \"1%2F4\"
\n" ); document.write( "\"2%2Fa\" = \"1%2F4\" - \"1%2F8\"
\n" ); document.write( "\"2%2Fa\" = \"1%2F8\"
\n" ); document.write( "a = 16 hrs working alone
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "You can confirm this yourself using the 1st equation
\n" ); document.write( "\"8%2F16\" + \"8%2F24\" + \"8%2F48\" = 1\r
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