document.write( "Question 728564: A machine caps a 1000 bottles in 10 minutes, another machine caps 1000 bottles in 8 minutes.
\n" ); document.write( "a) If these machines were together how much time will it take to cap 1000 bottles?\r
\n" ); document.write( "\n" ); document.write( "b) if t1 and t2 are the time in the above problem. Determine the time taken by both machines working together?\r
\n" ); document.write( "\n" ); document.write( "Can you please help me? Thanks so much in advance:) \n" ); document.write( "
Algebra.Com's Answer #445507 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
>>...A machine caps a 1000 bottles in 10 minutes,...<<
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\r\n" );
document.write( "So the slower machine's bottle capping rate is 1000 bottles \r\n" );
document.write( "per 10 minutes or\r\n" );
document.write( "\r\n" );
document.write( "\"1000_bottles%2F10_min\" = \"1000%2F10\"\"bottles%2Fmin\" = 100\"bottles%2Fmin\"\r\n" );
document.write( "

\n" ); document.write( "another machine caps 1000 bottles in 8 minutes.
\n" ); document.write( "
\r\n" );
document.write( "So the faster machine's bottle capping rate is 1000 bottles \r\n" );
document.write( "per 8 minutes or\r\n" );
document.write( "\r\n" );
document.write( "\"1000_bottles%2F8_min\" = \"1000%2F8\"\"bottles%2Fmin\" = 125\"bottles%2Fmin\"\r\n" );
document.write( "

\n" ); document.write( ">>...If these machines were together how much time will it take to cap 1000 bottles?...<<
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\r\n" );
document.write( "Let that time be x minutes\r\n" );
document.write( "\r\n" );
document.write( "So their combined bottle capping rate is 1000 bottles \r\n" );
document.write( "per x minutes or\r\n" );
document.write( "\r\n" );
document.write( "\"1000_bottles%2Fx_min\" = \"1000%2Fx\"\"bottles%2Fmin\"\r\n" );
document.write( "\r\n" );
document.write( "The equation comes from:\r\n" );
document.write( "\r\n" );
document.write( "            \"%28matrix%284%2C1%2C%0D%0A%0D%0ASLOWER%2C%22MACHINE%27S%22%2CBOTTLING%2CRATE%29%29\"\"%22%22%2B%22%22\"\"%28matrix%284%2C1%2C%0D%0A%0D%0AFASTER%2C%22MACHINE%27S%22%2CBOTTLING%2CRATE%29%29\"\"%22%22=%22%22\"\"%28matrix%284%2C1%2C%0D%0A%0D%0ATHEIR%2CCOMBINED%2CBOTTLING%2CRATE%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "                100\"bottles%2Fmin\" + 125\"bottles%2Fmin\"\"%22%22=%22%22\"\"1000%2Fx\"\r\n" );
document.write( "\r\n" );
document.write( "                           100 + 125 = \"1000%2Fx\"\r\n" );
document.write( "                                 225 = \"1000%2Fx\"\r\n" );
document.write( "                                225x = 1000\r\n" );
document.write( "                                   x = \"1000%2F225\"\r\n" );
document.write( "                                   x = \"40%2F9%7D%7D%7B%7D%0D%0A+++++++++++++++++++++++++++++++++++x+=+%7B%7B%7B4%264%2F9\" minutes\r\n" );
document.write( "\r\n" );
document.write( "----------------------------------------------------------------\r\n" );
document.write( "

\n" ); document.write( "b) if t1 and t2 are the time in the above problem. Determine the time taken by both machines working together?
\n" ); document.write( "
\r\n" );
document.write( "\r\n" );
document.write( ">>...A machine caps a 1000 bottles in t1 minutes,...<< \r\n" );
document.write( "
\r\n" );
document.write( "So the slower machine's bottle capping rate is 1000 bottles \r\n" );
document.write( "per t1 minutes or\r\n" );
document.write( "\r\n" );
document.write( "\"1000_bottles%2Ft%5B1%5Dmin\" = \"1000%2Ft%5B1%5D\"\"bottles%2Fmin\"\r\n" );
document.write( "

\n" );
document.write( ">>...another machine caps 1000 bottles in t2 minutes...<<
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document.write( "
\r\n" );
document.write( "So the faster machine's bottle capping rate is 1000 bottles \r\n" );
document.write( "per t2 minutes or\r\n" );
document.write( "\r\n" );
document.write( "\"1000_bottles%2Ft%5B2%5Dmin\" = \"1000%2Ft%5B2%5D\"\"bottles%2Fmin\"\r\n" );
document.write( "

\n" );
document.write( ">>...If these machines were together how much time will it take to cap 1000 bottles?...<<
\n" );
document.write( "
\r\n" );
document.write( "Let that time be x minutes\r\n" );
document.write( "\r\n" );
document.write( "So their combined bottle capping rate is 1000 bottles \r\n" );
document.write( "per x minutes or\r\n" );
document.write( "\r\n" );
document.write( "\"1000_bottles%2Fx_min\" = \"1000%2Fx\"\"bottles%2Fmin\"\r\n" );
document.write( "\r\n" );
document.write( "The equation comes from:\r\n" );
document.write( "\r\n" );
document.write( "            \"%28matrix%284%2C1%2C%0D%0A%0D%0ASLOWER%2C%22MACHINE%27S%22%2CBOTTLING%2CRATE%29%29\"\"%22%22%2B%22%22\"\"%28matrix%284%2C1%2C%0D%0A%0D%0AFASTER%2C%22MACHINE%27S%22%2CBOTTLING%2CRATE%29%29\"\"%22%22=%22%22\"\"%28matrix%284%2C1%2C%0D%0A%0D%0ATHEIR%2CCOMBINED%2CBOTTLING%2CRATE%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "                \"1000%2Ft%5B1%5D\"\"bottles%2Fmin\" + \"1000%2Ft%5B2%5D\"\"bottles%2Fmin\" = \"1000%2Fx\"\"bottles%2Fmin\"\r\n" );
document.write( "\r\n" );
document.write( "                           \"1000%2Ft%5B1%5D\" + \"1000%2Ft%5B2%5D\" = \"1000%2Fx\"\r\n" );
document.write( "\r\n" );
document.write( "The LCD is t1t2x\r\n" );
document.write( "\r\n" );
document.write( "                           1000t2x + 1000t1x = 1000t1t2\r\n" );
document.write( "                 \r\n" );
document.write( "Divide through by 1000\r\n" );
document.write( "\r\n" );
document.write( "                                   t2x + t1x = t1t2\r\n" );
document.write( "\r\n" );
document.write( "Factor out x on left\r\n" );
document.write( "              \r\n" );
document.write( "                                  x(t2 + t1) = t1t2\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by (t2 + t1)\r\n" );
document.write( "\r\n" );
document.write( "                                    \"x%28t%5B2%5D%2Bt%5B1%5D%29%2F%28%28t%5B2%5D%2Bt%5B1%5D%29%29\" = \"%28t%5B1%5Dt%5B2%5D%29%2F%28%28t%5B2%5D%2Bt%5B1%5D%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "                                    \"x%28cross%28t%5B2%5D%2Bt%5B1%5D%29%29%2F%28%28cross%28t%5B2%5D%2Bt%5B1%5D%29%29%29\" = \"%28t%5B1%5Dt%5B2%5D%29%2F%28%28t%5B2%5D%2Bt%5B1%5D%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "                                     x = \"%28t%5B1%5Dt%5B2%5D%29%2F%28t%5B2%5D%2Bt%5B1%5D%29\" minutes \r\n" );
document.write( " \r\n" );
document.write( "That's the answer.\r\n" );
document.write( "-------------------------------------------------------------------------  \r\n" );
document.write( "So the formula is \"the product of the times over the sum of the times\":\r\n" );
document.write( "\r\n" );
document.write( "We could have used that formula to solve (a) if we had had it, with\r\n" );
document.write( "\r\n" );
document.write( "t1 = 10 and t2 = 8\r\n" );
document.write( "\r\n" );
document.write( "                                     x = \"10%2A8%2F%2810%2B8%29\"\r\n" );
document.write( "                                     x = \"80%2F18\"\r\n" );
document.write( "                                     x = \"40%2F9\"\r\n" );
document.write( "                                     x = \"4%264%2F9\"minutes  \r\n" );
document.write( "\r\n" );
document.write( "Edwin
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document.write( "
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