document.write( "Question 1028975: Three machines are filling water bottles. The machines can fill the daily quota of water bottles in 90 h, 99 h, and 110 h, respectively. How long would it take to fill the daily quota of water bottles with all three machines working? \n" ); document.write( "

Algebra.Com's Answer #644043 by josmiceli(19441) $\"\"$ $\"About$

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Add their rates of filling
\n" ); document.write( "to get rate filling together
\n" ); document.write( "rate fore each machine =
\n" ); document.write( "[ daily quota ] / [ time to fill the quota ]
\n" ); document.write( "Let $\"+t+\"$ = time in hrs to fill quota
\n" ); document.write( "with all 3 machines working
\n" ); document.write( " $\"+1%2F90+%2B+1%2F99+%2B+1%2F110+=+1%2Ft+\"$
\n" ); document.write( "Multiply both sides by $\"+90%2A99+%2A110%2At+\"$
\n" ); document.write( " $\"+99%2A110%2At+%2B+90%2A110%2At+%2B+90%2A99%2At+=+90%2A99%2A110+\"$
\n" ); document.write( " $\"+10890t+%2B+9900t+%2B+8910t+=+980100+\"$
\n" ); document.write( " $\"+29700t+=+980100+\"$
\n" ); document.write( " $\"+t+=+33+\"$
\n" ); document.write( "with all three machines working, you can
\n" ); document.write( "fill the daily quota of water bottles in 33 hrs
\n" ); document.write( "-------------------
\n" ); document.write( "check answer:
\n" ); document.write( " $\"+1%2F90+%2B+1%2F99+%2B+1%2F110+=+1%2Ft+\"$
\n" ); document.write( " $\"+1%2F90+%2B+1%2F99+%2B+1%2F110+=+1%2F33+\"$
\n" ); document.write( " $\"+.011111+%2B+.010101+%2B+.009090+=+.030303+\"$
\n" ); document.write( " $\"+.030302+=+.030303+\"$
\n" ); document.write( "OK -error due to rounding off\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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